I am assuming that this is a relitively small (under 25kW) set for standby or remote location. If so it is unlikely that it is an induction generator. Induction generators are asynchronous machines which must have excitation from an active AC power line in order to work. They are not self excited and are commonly used in co-generation or other applications while tied to the grid.
It is likely that your generator has an exciter built onto the same armature as the AC winding. If you pull the brush cover on this type of set you will see a normal DC segmented commutator and a set of slip rings beside it. 2 if it is a single phase machine, 3 if it is 3 phase.
The DC side generates direct current to both excite the unit and charge the starting battery. Larger machines use different schemes with a rotating field where the AC is taken off the stationary windings and the DC excitation side of things may be entirely in the rotor with a set of rectifing diodes.
If you have the former kind of machine, check to see if the DC side is producing power first, if so check the wiring to the stationary field windings. The field poles should have sufficient residual magnetism to bring up the DC voltage, if not the field winding will need to be flashed with a car battery or some such. Lift the DC brushes, find the field leads and give them a quick flash with the car battery.