Use "i.e." to mean "that is" or "in other words." The abbreviation actually stands for "id est," which means "it is" or "that is," so it's pretty much a literal translation. To remember, think of "i.e." as standing for "it es," as though pronouncing "is" a little oddly.
Use "e.g." to mean "for example" or "such as." The abbreviation stands for "exemplum gratia," which more or less means "for example." Think of "e.g." as standing for "example gratis (free example).
Use "et al" to mean "and others." This is an abbreviation for "et alii/alia," which does mean "and others" and is used most often when you want to shorten a list of people, often authors of an article. For example, "Jones et al found that global warming is happening." Remember "et al" by thinking of the words "and all," which sounds similar and will remind you of the meaning.
Use "etc." sparingly in formal writing.It stands for "et cetera," which translates to "and the rest," but students and lazy writers often make the mistake of using "etc." when they can't think of a third item to put in a series. Instead, use it only for longer lists, such as in this sentence: "The groceries included bread, soda, milk, etc."