When you enter a short contraction (I'm, I'd, etc.) or a longer one where there is no ambiguity (don't, aren't, etc.), don't bother entering the apostrophe. The autocorrect feature will "know" that you're trying to enter a contraction and offer you the correct word as an alternative. So, for example, when you enter "im" it will offer "I'm" and when you enter "dont" it will offer "don't".) When this happens, all you have to do is hit the space bar to enter the correct word.
Unfortunately, you can stump autocorrect with words like "well" and "were" (words that are legitimate with or without apostrophes). In cases like these, if you mean to enter the contraction, duplicate the last letter of the word when entering it and autocorrect will offer you the contraction. For example, if you mean to enter "we'll" key in "welll" and hit the space bar. If you mean to enter "we're" key in "weree" and hit the space bar.
This technique saves you from having to go to the symbols keyboard to manually enter the apostrophe.