Do you have your landlord's approval? If not, that would be the first step. Many owners would want to interview the new prospective tenant before granting permission for a sublease. If you live in a complex with a management company, it may be even more difficult. Whatever the circumstances, do not go behind the owner's back ... it could be a very expensive lesson.
Assuming that it's OK, I'd post it on Craigslist or one of those "green sheets" found in many restaurants and convenience stores. I own several rental properties, and would not want to lease any of my homes to a stranger. Best of luck ...