Oxy-acetylene welding (also known as gas welding) is not super common anymore as most welding today is arc welding. This type of welding relies on combustion of oxygen and acetylene to melt 2 pieces of metal together.
You don’t need power to do this type of welding, just 2 securely fastened tanks (one with oxygen and one with acetylene).
The easiest way to get into welding is to look up classes at independent art institutions, trade schools, or community college courses. An introductory course can get you set up on all the essentials like safety procedures and technique.
Buying an at-home welding kit is relatively inexpensive and can end up being a relaxing hobby or a useful skill for repair things around your house, yard, or even your car.