Here's how, and it's all available at your website or department store of choice (cough cough Amazon, Wal-Mart)
One (1) marine deep cycle battery, as large as you can afford
and/or can carry (approx $80) (must buy in store)
One (1) 12 volt trickle charger (approx $30)
One (1) 12 volt to 120 volt inverter, sized according to your needs. 200 watts will power a few devices for around $40; do yourself a favor and get a 600 watt Tripp Lite or similar, around $90
Optional: One or more 12V accessory plugs, to wire into battery (approx $10/ea)
My current "Power Box", pictured below, is currently out on an off-grid island staged and waiting to run some Civic Wireless customer premises equipment. The box will run network gear on a small inverter for weeks on a full charge.
Part 2: Exploring solar trickle charging.
Questions? Email: help [at] civicwireless.org
Pretty sure the title and image says it all. This guy is hardcore!