Check to ensure that the CFL is completely intact. If the CFL is simply burned out, you do not need to take precautions insofar as personal safety is concerned. The mercury amount in CFLs is minimal and will not escape from an intact bulb. Simply remove the bulb from its socket and set it aside for recycling.
Locate your nearest CFL recycling location. The EPA has some websites to help you locate the site closest to you. You can also contact your waste pickup service directly; if you don't know the contact information for your waste service, you can find it through your local government.
Take precautions when cleaning up broken CFLs. The EPA recommends you clear out the room where the broken CFL is, turn off the heat or air conditioning, and open windows to air out the room. Wear gloves when you carefully pick up every piece, no matter how small. Place the pieces in two plastic bags or another container that you can seal. Place the sealed container outside in a safe place until you can get the pieces to a recycling center to be disposed of properly.