Our forklift works perfectly in reverse but rarely goes forward. Where do we start?
You're going to have to provide a whole lot more information than what you have. What model, controller, pics if any. If you don't have the info then post pictures of the controller, contactor panel, directional selector and what ever else you have. Way to many models to generalize.
Here are some basics in understanding electric forklift diagnostics: http://store.intellaliftparts.com/blog/understanding-electric-forklift-diagnostics/
Most of the Yorks I worked on were contactor/resistor setups, built before electronic controls. If yours is a contactor machine then you need to check the forward reverse switch and the coil and silver plated contacts on the forward contactor relay. Does it make a clunk noise in both forward and reverse when you first move the speed control/throttle pedal? I even had the luck to work on a couple drum control machines way back, those were the ultimate in simplicity, rugged, lasted almost forever and were extremely reliable. Couldn't have that, we had to "improve" on it until nothing works right anymore, lol.