did the ad (or whatever) give you any guidelines? even if they're vague, stick to them.
what is a "traineeship sort of thing"? will you be getting paid? do you have to interview? is it a covering letter for a resume? etc.
google search for "cover letters" produces 153 million hits. surely one of those at least gives you a starting point?
i'll be quite frank with you - your original post suggests you put absolutely no thought into this at all before you asked for help. just post a question on bluelight and let others do the work for me. remember, i don't know anything about you - that's just how posts like this come across to me.
my advice is to consider all the information you have about the position, the company, the person who will be reading the letter, etc. then draft a version and post it asking for criticism.
it's my humble opinion that this is much more likely to generate a helpful response.
how many people will you be competing against, if any, to get this position? if they've all just posted on a discussion and sat back and waited for answers, maybe you've got a chance. this doesn't have to be wall street but a little bit of motivation on your part might reap enormous rewards. find out who's going to be reading this letter... find out if they have a secretary? go talk to them and ask them for some advice on writing a successful letter specifically for this person... what will succeed...what will fail... etc.
ok, perhaps it's a little wall street but it depends on what's at stake here and how badly you want it.
i've made a lot of assumptions.if they are wrong, i apologise. let us know how you get on?
alasdair