(Of course this goes without saying but I'll put it in here anyways, ALWAYS UNPLUG AND DISCONNECT YOUR COMPUTER BEFORE INTERNAL SERVICE.)
What we do for our clients is take the computers back to our shop, and use an air compressor to blow the dust, fur, and other buildup out of the casing.
The only caveat to this is you want to make sure you hold any FANS in place so they do not spin freely. The air speed a compressor sends through them could be more than what the Fan is rated for and you'll damage the bearings.
After that we take Q-tips and clean the heat sinks (big blocky metal things) and other hard to get areas. Then we let it sit long enough for the cleaning solution to evaporate off, and power it back on to confirm everything is still connected, and out the door it goes to another satisfied customer.