Easy way to clean a DualShock 3?
Solution 1:
Don't be too afraid to open it up. I've had to open mine a couple times to replace thumbsticks destroyed by my son. iFixit has some great guides for replacing almost every internal controller component. The hardest part is getting the pieces that fit between L1/L2 and R1/R2 back in and secured.
Solution 2:
If you want a thorough clean but don't want to open your controller, I recommend trying a product called Cyber Clean, it's a silly-putty like product which you can squeeze into tight spots and when you pull it out, it picks up dust, hair and other stuff that might get inside your controller. I've used it on my keyboard and it works. It doesn't compare to a thorough take-your-device-apart cleaning, but it's better than just wiping the outside.
If you do decide eventually to open your controller to clean it, make sure not to use anything that might damage the circuitry, and take care when taking the controller apart, the shoulder button springs tend to fly out. Also, opening your controller will probably void its warranty.
Solution 3:
If you want a purely mechanical cleaning technique that doesn't involve dis-assembly or solvents, then one way that I've used in the past is to take an index card or similar, and curve it to match the curve of the button, then rotate it around the button while it is pushed into the controller. It may take multiple cards to get most of the sticky stuff out, and it often won't get everything. It usually does improve the feel of the button however and reduce the frequency of it getting stuck.