It's quite a while since my hubby's done this job, but you'd first need to be qualified as an operator on each type of truck you'd be training on - counterbalance, reach, rough terrain etc etc. You'd also need to have an instructor certificate for each type of machine. I think the governing body is the Association of Industrial Truck Trainers (AITT). There are commercial organisations who will provide this training, but it's not cheap unless you can get someone to sponsor you.
It also helps your employability if you can offer skills in areas such as manual handling, crane slinger/signaller, cherry picker (sorry, I can't think of the 'proper' name) etc. Hubby started out just doing basic and reach forklifts, but his employer paid for him to qualify on a wide range of machines during his time there, and he ended up training on pretty much everything, including excavators on building sites.
Hope this helps.