Obviously you will need an old pair of speakers. The foam surround kits are not inexpensive so make sure you are getting a decent pair of speakers to begin with. Also the paper cones should move freely and they should still make sound when played. All the drivers should play. If they have been energized a lot with the surrounds damaged, the voice coil could be abraided away, shorted out, etc. Those should be avoided because I don't think that's an easy fix. Today we are working on a pair of Advent Heritage speakers. They are not the classic Advents and were produced after Jensen bought the company and ruined it. However these speakers, despite, their shortfalls, sound really good to my ears. The cabinets are pecan and clean up really well.
Razor blade, hobby knife, or scalpel
Stiff brush or toothbrush
Can of air
Speaker refoam kit http://stores.ebay.com/GeoAli-Vintage-Stereo-and-More
The kit I purchased included the glue, paint brushes, shims, speaker edges, and instructions.
Wood care products of choice (I'm using Howard's Restore a Finish and orange oil cleaner)
Clamps, c-clamps or the like if you have beauty rings to clamp into place.
Hair dryer or heat gun if your speakers have vanity rings around the basket ring.