Can I upgrade a Hercules Dirtrider 26" with gears and a disk brake?
The derailer is sort of the easy part. Your frame could take a claw style derailer like this:



Or you get one of these and have a lot more options:



120mm is the minimum rear spacing for derailer multi-speed rear hubs, so you would probably need to spread (bend) the frame.

You'll also need a new rear wheel, chain, and freewheel. Your cranks will probably not give workable chainline with a multispeed freewheel as they are now, which usually means toying with the BB spindle length, which is a pain on cottered cranks, and would probably also have you either removing the chain guard or finding a way of spacing it out.