How do I connect my replacement 3-way switches?
It sounds like your setup is like the following:



You seem to have the source coming to one, and then being looped to the other switch. Often time what happens in homes is that other devices get joined at a junction box. The "extra wires" you are mentioning are more than likely going to other devices and the box is just providing a spot to do so. 

You will want to turn off the power to the switches and determine which wire goes where (for the other devices) and which ones goto your light and other switch.