If you want to go the ghetto route, you can just get audio extension cords and run them from each computer to a point where you have cables coming from the speaker system. Just hook up the input you want to use at the time.
If these are 2.1 speakers, you could run the output of one computer to the line-in of the second. Mute line in when you don't want the audio from that computer. This would also work for multi-channel systems if you have a mode on your soundcard that will map stereo to all the speakers (although you'll lose true surround effects)
The best solution is to get something that will select inputs and only allow one through at a time. Unfortunately, I haven't come across anything that's affordable in that department. It's probably going to cost over $50 to get a solution like that running, which is kind of a lot if you ask me. Most selectors you can get are for HT stuff and are therefore RCA inputs, so if you got one of those, you'd have to get 1/8" to RCA adapters for all the inputs and outputs = even more expensive.
If you don't mind connecting a couple cables when you want to switch, I think option #1 is the most affordable and easiest.