Compliment (a remark that says something nice)
Complement (something that completes something else or makes it better)—notice that the beginning of this word matches the beginning of “complete.”
Stationary (motionless, still)
Stationery (the things needed [often referring to the paper stock] to write a message)—notice that this word has “er” in it, much like “paper” does.
Principle (a moral belief or an idea that is the basis of a theory)
Principal (the head of the school)—I like to look at the ending “pal” and think of the principal as my pal.
There are, obviously, many more homonyms ready to trip you up, and if you want to come across as knowledgeable about your subject, you’ll want to get it right. So when you’re in doubt, you should always look up the word to be certain. If you need a jumping-off point, this guy seems to have a pretty good list. Scoot on over to his site or to any other resource to get a sense of which word to choose. And then you’ll be on the road to more precise writing.