By remembering three easy cheats:
2.) They're is the contracted form of they are (the apostrophe stands in for the a in are — see my post about apostrophes), so if you mean they are, use they're.
3.) Their is the only one left, so it should be easy to remember, but if you must have a cheat for it, here it is: Their heir is going to inherit a lot of money. If your word means they own or possess something, then use their.