If I was involved in an accident, how is it determined who was at fault?

There is no simple, right or wrong answer about fault--it always depends on the exact situation. It could be either of your fault, or, more likely, you both share fault to some degree, which impacts how much each could recover in a lawsuit. For example: driving without lights, if at night, would be careless or negligent on his part--that argues in favor of his fault (if during the day, it probably doesn't make a difference). Your car suddenly stalling in front of him would only add to his fault if the reason he couldn't stop was either that he was going too fast or saw you turn and kept going when he should have slowed or stopped to let you do that.

On the other hand, if even without his lights, visibility was good enough to see his car, then if you turned left across traffic when an oncoming car was near, that argues in favor of your fault. Or if the car stalled because of poor maintenance by you, because you made an error driving (e.g. a  stick shift and you stalled it out), or because you'd forgotten to fill it up, those also argue in favor of your liability or fault.

In short, it depends entirely on the circumstances, and from what you write, it is plausible you both share fault. An experienced attorney can help you understand your rights, recourse, and also exposure. Good luck.