I learned to weld, not professionally, on a stick welder. You should first go to a local library, check out books on welding, and read up on the subject. Welding consists of technical knowledge about metals, etc, and then learning techniques, then developing manual skills through practice.
Re welding away from power, Lincoln use to make a model called Weldanpower which was a combination generator and welder. The generator could be used as a power source but I don't remember the capacity and i don't know if anything like that is still made. It was fairly inexpensive, but there are larger expensive models.
KEH