So you suddenly notice that your FIOS box, usually mounted in your basement or garage, is beeping. On closer inspection, the red replace battery light is on. If you call Verizon, you will also learn that they will not replace the battery, it is your responsibility. They will sell you a new one, but it is not cheap.
Now that you know this, you have two options that will save you a lot of money. The first is to simply reset the unit. It seems that the FIOS box will often erroneously report that you have a bad battery, when you actually do not. To do this, unplug the FIOS box. Then open the battery compartment. Inside will be the sealed battery with two wires coming from it. Remove either the black or red connector, it may be easier to do if you slightly remove the battery by pressing down on the two plastic clips holding it place. Then wait for a minute or two after unplugging the battery. Then reconnect, close up the panel, and plug the box back into AC. At this point, you most likely will notice that the red light goes out, and no more beeping.
If this does not work, it means your battery is bad. You can buy a replacement locally, or order from Amazon here. To install, remove power, open box, and remove both connectors. Remove the battery and replace with the new one. Make sure you hook up the red lead to the positive battery terminal, and the black lead to the negative. Close everything up, and turn back on. Congratulate yourself on saving some bucks and eliminating the annoying beep.