Audio input switcher box?
 

For xmas I picked up a monitor that has HDMI in and audio out via 3.5mm speaker jack. I only have one set of computer speakers so when I happen to be playing the PS3, I have to unplug my computer speakers from the PC and plug it into the monitor. Is there some kind of hardware device or something where I can plug both the PC and the monitor into, and an output line to the speakers so all I need to do is push a button to switch the source of the audio?

Yes. There are gazillions of such products.

Better options would be:

a) Feed both into a 3.5mm Y-cable. 3 bucks at a parts shop. Make your own for less than two.

b) PS3 to computer's line-in audio. Free!

How would I get the ps3 to computer's line-in audio? I have an optical out my pc, and audio out imputs. Not sure if I have an audio in, and the ouputs on the PS3 are the ps3 RCA jacks, hdmi and optical

Two RCA female to one 3.5mm male Y cables or can be had for the same price as above if you don't have the spare part lying around somewhere. Your computer will have a 3.5mm line-in input, very likely right next to your microphone input.