Eventually, your droid will begin to complain with a Low Power fly text when its battery has worn out.
Most of your droids functions will not operate unless it has power; it will not respond to voice commands, will not learn its name, and most modules will not function.
The only modules that will work when your droid has no power are the Crafting station modules and storage modules if you have them installed.
Droid Battery[]
To recharge your droid, first you will need a Droid Battery.
You can usually pick up one of those from the same place you found your droid. Most engineers will offer them in crates.
Make sure that you have the battery in your base inventory -- meaning not in a bag or container. Next, call your droid and open up its Radial menu. Select the menu option 'Droid Options' and you will see a Recharged fly text. This should power your droid back up to full. You can double check by opening up the examine window for the droid. It should list the droid at 100%.
EG-6 Power Droid[]
One can also use the EG-6 Power Droid to recharge other droids, by programming him with the "Recharge" command in the Radial menu under "Program", and targetting the droid you wish to recharge.
Note: As of GU5, the recharge feature through the EG-6 Power Droid is not working