You'd need to get yourself qualified as a) an operator and then b) an instructor for each type of truck you want to train on, plus it's also good if you offer things like manual handling and hazchem etc.
My bloke did the job up until five years ago, and then he'd had enough - spent a good deal of time training really nice people, only for their companies to make them redundant a month later. Half the time he knew it, but the trainees didn't and he hated that.
Many people who do it are self-employed. I think the work is out there, but it's quite jealously guarded.