It's called an apostrphe. It's very common to use it after the personal pronoun "I". For example, I'm using it now. OR I am using it now. It used frequently in English for contractions, e.g. can not = can't
It can be used in the contractions RonBee has given, but it shouldn't be used in formal English. I'd never use a contraction in a letter or piece of professional writing like a report or in any academic writing. It's fine in emails that aren't formal or on a forum like this, but elsewhere, I'd stick to the full forms.
BTW, 'I'd' can be either I had + past participle or I would + infinitive without 'to'. And do remember the old exam trap 'I'd better', where it is 'I had', while in 'I'd be better...' it is 'I would'.