Transformers are your friend!
Easy peasy, if the numbers work.
Start by looking at the air conditioner. You need to know the number of "watts" the air conditioner uses, probably between 1000 and 3000. This number is often called VA instead.
Next, look at the receptacle (outlet) on the generator. If it looks like the totally common AC power outlet, then you can't do it if the A/C unit takes more than 1800 watts.
If it has an extra horizontal bit (like this), then you can't do it if the A/C unit takes more than 2400 watts.
Next, you'll need a 240-120V step-up/down transformer whose watts (or VA) rating is larger than the air conditioner. You set the transformer for 120V input, plug it into the generator, and plug the 240V A/C unit into the 240V receptacle on the transformer.
There's one more hitch: what's the capacity of the generator? (again in watts or VA). If the generator doesn't have enough watts, then it cannot start the air conditioner. That's likely. Generators which are 120V-only tend to be small, and air conditioners which are 240V tend to be large.
(By the way, most 240V window air conditioners are 240V-only, don't need neutral, and use a NEMA 6 connector. I've never seen one that is NEMA 10 or 14 needing neutral.)
