[MichaelP]

They run on 12v batteries, car batteries. You can buy them 100 watt up. For the devices you want a 300-500 watt would work. They'll tell you what you can plug in. Keep in mind that the higher the watt rating the faster your battery discharges...Cost $30 to 100$ at walmart.

Mike

[Blood of Tyrants]

The others are telling you straight scoop. The inverter converts DC (battery) to AC (house current). If you get one big enough to run an LED lamp, a computer and your modem (I would guess that you need to power it to stay connected to the Internet, you would need one one in the 300-500 watt range. But be advised that the inverter turns low voltage DC current into high voltage AC current and there will be a significant current draw on the battery( 25 t0 40 amps) and it will discharge fairly quickly. You will need the largest deep cycle marine battery you can find.