I dare you not to run the motor at all, before doing a bit of safety inspection first. The insulation on the wires is falling apart and the wire insulation inside might be compromised too.
So start by dismantling the motor and checking what the inside looks like. Then replace carefully the leads coming out of it. Check insulation resistance with a megger.
Then if all that is done, first you need to figure out the type of the machine, so you will be able to wire it accordingly: From the photos it seems it is plain simple induction motor, single phase 115/230V with a run capacitor (that is the big can on the top. The cap should be checked too and preferably replaced).
The wiring is not clear to me from the photos, would need to measure it with ohmmeter first, to figure what is connected to what. Could you please do that first? Measure all the windings there and draw a picture of what was found. Then it will be much clearer how it is supposed to be connected.
//EDIT: Seems only the wires from the run cap are falling apart. Still, should be changed (probably together with the old cap) without a thought.