Usage 1: An expression that uses litotes is "litotic" and one can speak "litotically." Litotes is a form of meiosis "understatement," the opposite of "hyperbole" or rhetorical exaggeration. When Tom Jones sings "It's not unusual" when he means "it is usual" he is engaging in a perfect example of litotes. While some instances of litotes may seem to be double negatives, this kind of double negative is OK since it serves an honorable literary function (as the next section explains).
Suggested usage: Litotes is a rhetorical trope which can be used for a not unsubtle effect. It can be used to soften the blow of an unwelcome truth as when your friend says that your blind date is "not unattractive." We also find a kind of ironic emphasis in reverse: "While I wasn't looking forward to that dinner party, the evening was not at all unpleasant." Not all litotic phrases involve double negative, as we see in Queen Victoria's classic British understatement, "We are not amused." Not too shabby, eh?
Etymology: From Greek litotes "simplicity" from litos meaning "plain, simple." The Greek root is based on PIE *(s)lei- "flat, slippery" which also underlies English "slime," "slick, "slice," and "slip." Old Irish sleman "smooth" is also related, as is Latvian slieka "earthworm." (Kudos for today's word goes to Grant Hutchison of Dundee, Scotland, a not infrequent visitor to the yourDictionary Agora at http://www.yourdictionary.com/cgi-bin/agora/agora.cgi.)