Quick tutorial:

Here's the mouse and fart-button i started with:

I didn't think of doing this write-up until after this was all done and the spare parts were trashed from the fart machine. So there are only before and after pictures...

1) take the fart button apart. There are some screws you'll see under the batteries and hiding under a sticker. Take them out and figure out how to get to the PCB. Take note of where the switch and battery were connected inside the case.

2) Once you have the PCB exposed (mine looked like this) disconnect the button mechanism from the plastic casing. Remove the PCB and speaker.

3) Crack open your USB mouse and peek inside. It should look something like this one. See the Red and Black on this little plug? That's our power. The red is going to go to the battery + and the black to the battery - connection on the fart button PCB. Go ahead and run the wires from the fart button to the plug. I just forced the wires into the back of the plug and taped them together. You could also solder these to the pads where the power connections land.

4A) (This is where versions 1 & 2 differ) I chose to hook my farter up to the right click button, for no reason but to add a little relief for the victim and a little anticipation for the prankster. To find the right side of the button to hook into, you want to either take a multi-meter and figure out which side goes to ground when the button is pressed. On this mouse its the outside legs.

Solder the gate pin of the transistor to the switched pin for the right button and connect the other two legs in the appropriate manor to the 2 leads that used to go to the fart-button's switch. (negative side of the switch to the emitter and positive side to the collector).

5) Cram the speaker in (you may have to bend out some tabs on the shell of the mouse here and there to make it work) and the PCB as well, making sure to not let the 2 PCBs touch anywhere (electrical tape works to separate as well). Screw it back together and plug it in.

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Version 2 -
Allows someone with no transistors lying around to still pull it off.

4B) Instead of useing the resistor, I just used some spare wire to create a mechanical switch inside the mouse. This ended up being more of a pain than it's worth, and I'd recommend just going to radio shack and picking up a transistor, but...

Take the grey plastic button structure out.

Make a small groove with a dremel or knife, or a hot soldering iron in one direction on the mouse housing and then at a 90degree angle to that on the grey button you wish to add the trigger to.

Solder the ends of these 2 wires to the places the fart-button switch was formerly connected to.  This just completes the circuit when these wires touch.

Continue with step 5 above...

--I must add that this way is less reliable and truly more effort in the long-run, but it does work and doesnt require any extra parts...