Depends where you're at. Best way to do so is by reporting the thread and let a mod close it for you. However, in some areas of the site you can close your own thread by going into "Administrative" I think and then closing it. An example of a place where you can close your own thread is in TBT Marketplace. =)
Others can probably give you better answers than me.
I click on edit on any post of mine, then click the one which says "Go advanced" or something similar. Scroll a little and it usually says something about closing a thread
Certain boards allow you to close your threads(TBT marketplace, Villager Plaza, and Retail.) Most of the others require you to report the thread(using the report button at the bottom of each post),to ask to close it.