Hello roolit,
Two usual ways to do that is to use either:
1.- Screw an nut to convert rotating movement into linear. The screw may be a recirculating ball type or a standard one. You must decide considering tolerable linear play, need of "reversibilty" in the sense that you can control load torque and not in the sense of going up or down. The recirculating ball screw is "reversible" and, usually, a standar screw is not.
2.- Using a toothed belt and wheels.
In any case, please consider the enviroment: presence of corrosive, inflamable or otherwise dangerous vapors, ambient temperatures, etc.
Hope this helps.
Regards!