Peter, who met the players on Friday morning and enjoyed a full day's work with them at Chadwell Heath, also speaks of:
* What life was like as Paolo Di Canio's room mate when he was a Celtic player.
* How he reacted when Alan Pardew took over Reading - and dropped him.
* Why his move from AFC Bournemouth was brought forward.
* Where he feels he can help the players improve.
Speaking following a double training session under Alan Pardew's watchful eye, Peter enthuses:
"It has been fantastic and it has been an exciting time for myself and the players, I feel, because there are obviously some new faces there apart from myself.
"Hopefully players like Jermain will get a lift - I know him from my time at Bournemouth when he was on loan, so it was nice to see him again.
"From a personal point of view it is great to get involved with a club that has such a high profile and with such expectations.
"That's what you want to be involved in - you want to be right at the crux of things and I was delighted to go on that training field today."
Peter's voice is already hoarse from shouting encouragement - we trust he will have a gargle before Sunday - and Scotsman Peter smiles:
"One thing people will have to get used to is that I am very vocal - and the biggest problem people are going to have is understanding me."
West Ham fans are also in for seeing some physical, as well as verbal, antics in the technical area, and Peter adds:
"That was the way I played; you don't believe you are doing it 99% of the time but I like to be involved all the time and I like to get my message across.
"Perhaps with Alan being on the touchline that will calm me down a little bit; when I am on the touchline I seem to be the 12th player, really."
Peter makes no apologies, despite West Ham being eighth, of insisting the Hammers can still come top, and he adds:
"The bottom line is that we want to be going into the Premiership as champions, and if you set your stall any lower than that is is failure as such - because, as they say, you have to aim for the stars.
"If you end up second then okay, you are still promoted, and if it happens through the playoffs it is still promotion.
"But there is nothing better than winning - and winning championships is the ultimate goal at the start of the season when everyone starts with equal points.
"When you start a race you want to win it - and we are no different."
The former Celtic stalwart's arrival comes in the midst of a flurry of transfer activity, and he adds:
"There has been a freshness been brought into the club players-wise and that gives everyone a big boost.
"I was at a big club that always brought in fresh players, even when you were successful, and there was always a buzz about the place because players knew they had to improve to keep their position.
"It gives them a lift and an incentive when they hear different voices around them and hopefully that is the thing that is going to shine through in the next few weeks."
Peter knows he has to help cure the relegation hangover and adds:
"There is no doubt that there has been a massive disappointment because West Ham are a massive club, but at the end of the day the name is not going to get you results.
"You have got to perform on the pitch and just because you are West Ham United you have no divine right to win a game of football - you have to earn that, and I think the harder you work the luckier you become.
"The fortunate thing is we have got a fantastic fan base who are desperate to do well and on the other side when you are not winning games it can be a tricky situation."
Peter says class alone is not enough, and adds:
"As well as we have the actual technical ability you have to have the mental strength to play in front of such supporters, knowing that if you produce the goods here you will get the rewards.
"There is bundles of talent and energy there, a real usefulness about the place, and the experience you need to be successful - so there is a great mix there.
"You are hoping that enthusiasm allied to ability can be married together and we can become a very good side."
Peter is well aware of West Ham's footballing traditions and says:
"We want to be a side built on the West Ham tradition which is not only winning games - but winning with style, as well, and that is what we are trying to instil.
"You want to win games whichever way you can but I played at a club very similar to West Ham and there is a tradition of playing very good football.
"The fans here demand that and we have to give 100% commitment."
Talking of the timing of his move from Bournemouth, he explains:
"It came right out of the blue; I think it was Monday or Tuesday when Alan asked me if I would be interested and he didn't have to ask me twice.
"It was going to happen over the next two weeks because Bournemouth wanted me to stay for the QPR and Plymouth games as they are top of the table, then it was agreed I would stay for the QPR game, then the story broke and they wanted it cut and dried as I did.
"I am delighted I have been here to get my first day on the training pitch and I want to get on with the job and do what I am here for, which is try and help the players get better and hopefully progress the team."
West Ham have good relations with the Cherries over the years, with, amongst others, Matt Holland, Steve Jones, Steve Purches, Rio Ferdinand and Jermain Defoe going to Dean Court, permanently or on loan, and Peter says:
"They are a fantastic club and I have nothing but praise for them; the manager has been first class to work with and gave me great knowledge of the game on the coaching side.
"He didn't stand in my way because he knew what a great opportunity it was for me, and they are similar, on a smaller scale, to West Ham - they like to play the game in the right way and they pass and move the ball non-stop.
"When I was at Bournemouth one of the clubs you looked up to was West Ham because of their traditions; I know people talk about the Harry link but I think the biggest link is the way they play the game of football."
West Ham have had plenty of links with the club Peter played for over 500 times, Celtic - one of whom is former folk hero Frank McAvennie.
"I got a phone call from him yesterday," says Peter, "and he told me he was coming down and to pass on my regards to everyone.
"But I said that means they will all know I am a friend of yours and I don't know if that is a good thing or a bad thing!
"But he has been fantastic and he was delighted for me; he will come to the training ground and it will be good to see him."
Paolo Di Canio of course played for both clubs, and Peter says:
"Paolo was a great friend of mine, a room mate at Celtic, and I know how much the West Ham fans loved him.
"He was a very, very close friend, a room mate and a half, and I know he has done a couple of pages in his book about myself because we were close.
"He talked about the fish episodes that we had, putting fish in my bed - a salmon's head the size of a shark - and chasing about the room.
"It was always lively and he was a very emotional man; sometimes you had to put him in his place but he played with his heart on his sleeve.
"Yes, I can understand people saying he was unruly, and I wouldn't necessarily say that in a bad way, because he would give his last.
"I had a fantastic relationship with him and I love the guy like a brother.
"Paolo Di Canio at his best was absolutely phenomenal and he was a joy to play with; I'm just disappointed that I missed the time he was here because I'd have loved to have been on the training field with him.
"You don't coach him, you just let him play and win you the game and I think he would have responded to that challenge - it is just a pity our paths haven't crossed here."
Another ex-West Ham player that Peter knows from his Celtic days is Stuart Slater, who went to Glasgow from Upton Park as a youngster.
"I knew Stuart Slater and I know he is still involved with the club at a younger level, so there is a big connection there and I think that is because both clubs have a tradition of playing the game the way it should be played.
"They have passionate supporters who are desperate to see you do well.
"At the end of the day he came as a young boy and maybe the timing wasn't right; he was talked about as being this or that type of player and I think that is a hell of a burden to put on someone - especially at a club like Celtic where there is massive expectation.
"And, to be fair, we weren't the greatest side then and to have got the best out of Stuart we would have needed to be a better side, to be perfectly honest.
"It was a bit unfair the way he was treated as a player because there is no doubt he was a wonderful talent."
Peter is firmly of the opinion that playing the right way is important, and he adds:
"I think that is one of the reasons he brought me in; if you watch Bournemouth at a lower level we want to pass the ball and work ever so hard - when you have not got the ball, and twice as hard when you have.
"When people see you doing that and creating chances they are happy; we have got the firepower here and an unbelievably talented squad who are all comfortable when they are in possession of the ball.
"Now we have to be able to do that in front of the home crowd and show them we are working in the right direction."
Peter has already been won over by the aura of the club and he says:
"What a place this is to play; when I drove into Upton Park last night I wanted to go and play; I wanted to say 'just let me out on the pitch - not as a coach, but as a player'.
"The place gets you going and you hope that rubs off on the players."
Peter has played under Alan Pardew at Reading and he recalls:
"I was very friendly with Tommy Burns who was a big pal of mine, and he got the sack.
"Alan came in as caretaker and we won the first three games, I think, and I had done very well, and then all of a sudden I wasn't even in the travelling 16.
"But I am not one that goes and bangs on the manager's door; I expect a manager to come and see me if he drops me for playing poorly.
"But I didn't think that was the case at the time; after a couple of weeks I went to him and said 'listen, if you have left me out of the team because I am playing poorly, I disagree with you, if you have left me out for different issues, I have no problem with that and I will deal with it.'
"I got back in the side and never looked back; I think he saw the sort of character I was and if I am left out of the side, hey, that's life.
"It is just a case of showing the next time you do get in that it will be difficult for someone to get my place back.
"That's about strength of character and maybe that is one of the reasons Alan brought me in."
With the home form disappointing this season, by Alan's own admission, Peter knows the players are under pressure.
"I have lived with pressure and for me it was 24 hours a day, seven days a week at Celtic, and that is the way you had to live it because you were a Celtic player 24/7.
"I was fortunate enough to be brought up in it so I understood it, but it was only when I moved away from Celtic the pressures that go with it.
"And then I understood why certain players with big reputations folded, really.
"The good thing I can put across to the players is that I have been in a position when things are not going as you want and the fans are on your case because they are so desperate for you to do well.
"They are not trying to be negative, that is just the way it is because if you are not winning games of football you can't expect them to stand there and clap you.
"You have to let them know they are not alone but the only way to get out of it is to go and play - don't be frightened of it, grasp it, because when you come out of the other side of it it is a fantastic feeling.
"When you go out there and the fans are starting to chant your name and you are winning you look back on the days when it was dark and you were under a little bit of pressure - and you enjoy the success even more.
"Hopefully we can instil that in them because if we can turn that corner, what a fantastic place to play."
Peter is looking forward to a full week at Chadwell Heath next week, and he says:
"The training ground is a great place to be; I am not one for saying 'this is what I'm going to do and what I'm not going to do' - you try and do your talking on the training field because at the end of the day you are playing with that big round object!
"Once you get that moving, football becomes universal and it is just a case of getting your points across and getting your players comfortable in the environment they are in.
"They need the comfort of being able to make mistakes if they are trying to do the right thing - and not be criticised for that.
"We are trying to bring the players back to the supporters and not have that aloofness; we are all here together and the only way to get success is if everyone is pulling in the right direction - it is a hell if a lot easier if you do it that way."
Peter is still taking in the fact that he has come to West Ham and he adds:
"I couldn't have written the script better and if you had told me this was going to happen a couple of years ago or a couple of months ago I would have said 'wake up'."
He can't wait for his first game at Wolves on Sunday and adds:
"It is two clubs with a massive tradition desperate to do well and what else can you ask for?
"It is the sort of game you want to be involved in and most definitely as a coach, being up against a Premier League team in a big cup tie."
The ultimate goal, though, remains promotion, and he adds:
"That is what we are aiming for; there is no one saying 'we are not going to be able to do this' or 'we are not going to be able to do that'.
"We are going in here to try and get in the Premiership, that is our ultimate goal, and we will do everything in our power to do that.
"You need that little bit of luck that goes with that and it will not be through lack of effort if we don't get there.
"If it is lack of ability in certain games or maybe the points that have been lost earlier in the season, you don't know but there are no excuses, we are aiming to get back in the Premiership as quickly as possible.