To avoid losing cellular service while on the road, keep a backup cell phone battery on hand, especially when travelling. This battery gives you additional power and talk time, should you run out before being able to charge your phone. Purchase backup batteries for your cell phone at most big-box and electronics stores.
Turn off your cell phone. It is possible to short out your phone when pulling out the battery and the phone is on (although this is not a strong likelihood).
Open the battery compartment on the back of the cell phone (the exact method for doing so is different for each type of phone) and expose the battery.
Remove the battery. This battery slides out just like any other battery found in an electronics device.
Insert the new battery and place the cover back onto the phone.
Power on the phone and the cell phone automatically detects the new battery and begins drawing power off it. (If this is the first time using the new battery there is, more than likely, only a half-charge or so.)