You "may" not need to change much. "IF" you have a "neutral" (grounded current carrying wire, usually white, NOT the green grounded conductor) wire at the machine after bringing the 220 V to the machine (takes four wires), then just lift the control wire at the terminal "B" as indicated on the diagram, and connect that wire to the neutral (that will be the only thing connected to that white neutral wire). No changes needed to the coils, they'll still be seeing 120V. If you can't bring the 120V neutral to the macine for some reason, then a small 240-120 step down transformer would be your best bet, in which case both A and B will need to be lifted, and wired to the 120V secondary side of the control transformer. Probably a 75VA transformer would be plenty big enough, be sure to fuse it with a small fuse (1 Amp or less). If you don't want to use a control transformer, you would need to replace BOTH coils in the reversing contactor to 240 coils, then the control wiring could stay the same.
Assuming the same HP for the motor (if you're replacing it), the overload heater will need to be rated for about half the amps that it is currently set for. However, most newer single phase motors have thermal protection built in (it'll say so on the nameplate if this is true), in which case you can just leave the existing overload in place.
Then, if your current motor will operate on 220V, just change the wiring according to the nameplate wiring diagram, verify that it reverses, and you're done. If it's designed to run only 120 V (unlikely), then you'll need to find an similar motor in 220V.
Most likely this will be an easy change to make. Take it slow, think everything twice, then go over the wiring again before turning the power back on. This is one of those things that is almost quicker to do than to explain, and I'm poor with communications.
