Usually you can write the first paragraph about how the writer came to know you and in what context. You can then write a second paragraph about your good qualities, what makes you stand out, etc. The third can just be a short reiteration about why you will do well.
Use "Sincerely," and leave a few blank lines so the writer can sign it (unless he plans on re-working it anyway). Put the date at the top under the letterhead, then the address you're sending it to, a reference line, and the "To Whom It May Concern:".
As far as vocabulary goes, just go for nice cogent thoughts that get your point across. It doesn't have to be a masterpiece, just a well thought out letter.