I live in a small apartment, and the kitchen is tucked away in a corner without any outside ventilation (windows or stovetop exhaust). Every once in a while I'll be cooking and something will start to smoke (a different problem, I know!) and the smoke detector will go off. How do I eliminate or reduce the amount of ambient smoke? I don't have access to external ventilation.
As SAJ14SAJ said, the best solution is to simply not live in a place like that - it can be a bit dangerous.
But since you're there, about the only thing you can do is get a decent fan and use it to direct air out of the kitchen toward rooms with open windows. Depending on the layout (and the fans) you may need multiple fans, and might want one of them to be a box fan in the window helping push air out.
For things you think may be smoky, you might also consider cooking outside if possible, on a hot plate, a camping stove, or a small grill. (Or you could just not do them at all.)