Single phase motors don't make good induction generators especially when you try to run them self excited.
You would probably do much better with a 3 phase motor even if you only need single phase.
As you have got it set up you might as well try it, it should work up to a point.
I take it that you are trying to self excite it using capacitors rather than trying to grid connect it.
You will most likely not be able to use the start winding unless you are very careful about capacitor values you connect across it.( you must disable the start switch if you want to try the start winding.
For a start I would try to get the run winding to self excite. Keep increasing capacitance until it builds up. You can run at nameplate speed or a bit more. Unless you have any frequency sensitive loads you may need to run a bit below synchronus speed to have a good compromise between volts and frequency. Nameplate speed will be a good starting point.
The more capacitance you add the higher the voltage and the worse the low load efficiency but the better it will maintain load. It should be ok for non critical loads but regulation will be poor and motor starting ability will be extremely limited.
If you can't get satisfactory results with the run winding alone you can add some capacitance to the start winding but check that you dont go too far , it will be easy to fry the start winding if it is intended for start only. If capacitor start and run then it will have a better chance, use the run capacitor but don't use the electrolytic start capacitor.
Induction motors are more suited to line operation, in which case they do have to run above synchronus speed and the poor regulation is no longer an issue.
They really are pretty poor stand alone alternators and are only suitable for loads such as portable tools and fixed load lighting. I wouldn't use them to drive anything critical unless it is a small percentage of a fixed load, in which case the voltage regulation may be good enough.
Good luck.