Check out the guide Shamoozal has put together that'll take you step by step through the cleaning process. You'll have to visit eBay again for a couple of tools (ironically one is an N64 Cleaning Kit), and pick up some simple things like q-tips and rubbing alcohol (what's in that Cleaning Kit anyhow? A damp washcloth?) and get to work.
Although you might spend more on the cleanup than you did on the actual console, making it look shiny like it was right out of the box = priceless. Folks will take one look and say N64? More like NEW64, amirite?