At most a screw drive and a soldering iron. If it isn't soldered then all you need is the screw driver.
I don't give a shit if you listen to me or not
Well it does matter on the ohmage of the speakers too, but if they are the same ohmage as the ones you are replacing, then all you should need is a screwdriver. If the ohmage is different, you're gonna have to re-wire the cab, but that's easy to avoid as long as you get the same ohmage of speakers as the ones you are getting rid of.
Quote by patriotplayer90
Will this involve many tools, or is it a relatively simple process?

Very simple. Quite time consuming if you don't have a powered screwdriver. About 20-30 screws in the back of a cabinet, well a 4x12 at least, and they go about an inch deep with a ton of threads...
Major of 7 String Legion 7 > 6

Carvin DC747
Ibanez RG2228
Schecter Avenger Custom Shop
and my baby....
Gibson Explorer Studio
It's MUCH easier than getting laid, depending on your personality.

But really...match the ohm and wattage loads for the replacement, unscrew the screws holding the old speaker in, and pull the leads on it. Put in the new one, screw it in, re-attach the leads.