How can you clean a cordless phone without damaging/breaking it?

First unplug the base unit so that you don't have to worry about hitting any buttons on the cordless. Then use a cloth that has been soaked in a cleaning solution (i.e. Mr. Clean) and water; wring the cloth out well and then carefully rub all of the surfaces of the cordless. For those hard to get at places use a dry Q-Tip underneath the cloth & rub gently.