Soundproofing requires mass and de-coupling. There are no shortcuts that really work. The good news is, of all building materials, the ones with the best performance are close to being the cheapest. I'm talking about sheet rock (about $4 to $5 per sheet, 4x8 feet) and MDF or particle board, about $10-15 per sheet depending on thickness. Resilient channel is more of a specialty item, and may be harder to find.
Anything you can do to add mass to either the top or bottom covering of the joists will help with sound deadening. If you have access to the upper floor, sometimes it's easier to add a layer of mass under carpeting than it is to add too much to the underside of the joists.
Some people use old sleeping bags, moving blankets, etc, to help deaden sound. They don't do anywhere near as good a job as what I recommended, and they are a major fire hazard. After seeing two people burned to death in a flash fire I will NEVER recommend anything that will burn quickly for inside building materials, other than minor wood trim...
