Normally, for AC motors:
- The stator will be wound with coils that are driven by the power line (sometimes with the aid of capacitors) to produce a rotating or just reversing field.
- The rotor will have internal coils that aren't directly connected to anything, but instead use currents induced by the fields of the stator and the rotor's "slippage" with respect to their alternation to induce currents in its own windings, "trapping" the rotating field and dragging the rotor along with it.
A typical conversion consists of replacing the laminate-and-heavy-bus-bar rotor with a magnet assembly - a total replacement, reusing just the shaft, or (typically, because it's less work and cheap) cutting off the outer part of the old rotor in a lathe, using the middle part as an iron core and mounting magnets on it (as was already pointed out). You'll find designs here for doing that several ways, the commonest being using epoxy to pot in bar or curved sector magnets, or fitting an aluminum sleeve over the cut-down rotor, with holes in the sleeve where round magnets are mounted.
Depending on the voltage you want, the magnets you can get, what voltage the motor was wound for, and what you're using to turn it, you might be able to use the stator as-is, or you might need to tear out the old coils and substitute new ones, with different wire thickness and number of turns, and/or perhaps wound for a different number of poles.
