How to power Arduino externally for long term?
There are several options for Arduino power in an external environment.


Wall wart: Connects to a wall socket, provides a great long-term source of power
Rechargeable battery: Doesn't last long, but they can be recharged and monitored with a low cost board
Alkaline Battery: Last longer, there are some monitoring systems available.
Solar: Only works when the sun is out, unless you combine it with a rechargable battery (example)
Nuclear power: NOT RECOMMENDED!!!