I've hacked about 1200 mice now, and this is how I do it...
For the most part, I essentially do the same as the other mouse hack tutorials and links mentioned so far. In the below pics, this is a 2.25" Happ trackball that I picked up just a little while ago. It had been left for dead when I got it; the Happ optic boards and the wire harness had been removed, the bearings were frozen solid, and the white ball was very dingy and scarred up. Side note: I soaked the bearings and shafts in penetrating oil (WD-40) for a couple days to remove the crude and rust. When I took the bearings out of the oil/sludge mix, they spun nice and free and the rust was removed from the shafts. Then I put the trackball back together using some old Happ boards I had and threw in an 8-ball instead of the original ball.
Back to the mouse hack...
Most importantly, use a multimeter to determine where the +5V and GND are on the mouse board before you remove any components. When working on an unfamiliar mouse, I decase the mouse and plug it into a PC. Be careful not to cause a short on anything with it plugged in, it can smoke your PS/2-USB port. Don't assume that the PCB plane is GND, I've run across PS/2 mice that have a "hot" board, and the GND is just specific traces. All the USB mice I've used so far have the more conventional GND plane, with the +5V only on specific traces.
I've seen some websites mention removing the LED from the board to "conserve power". DO NOT DO THIS if you want to follow my example. The below pics show getting +5V from the middle pin of the phototransistor location, which is very common with the shared-base style 3-pin transistors. On many mice I've seen, the middle pin of the phototransistor is powered from the cathode side of the LED, so if the LED is removed you won't have +5V at the middle pin location. Don't try to remove the LED from the circuit and replace it with a jumper either, just leave it alone, it doesn