Ce est la vie d' un pirate pour moi.
Because ce ends with a vocal and est starts with one it is shortened to C'est with an apostrophe. It is the same with d'un. There it would be de un, but since there are two vocals meeting each other there is the apostrophe killing the first vocal and the empty space between the two words.
Sooo this isn't explained in a very professional manner, but yeah, I hope it isn't explained badly