As other people have said, it depends on the bacteria and the amount of bacteria contamination. The classic food poisoning from the the potato salad at a hot summer picnic is the fastest (1-4 hours), but most infections take 8-24 hours to develop, some can take days.
Extensive table of bacteria and time of onset:
I thought you got sick the night you ate bad food?
Most people get sick 1-2 meals after the meal that was contaminated, but blame the last meal. Most bacteria need time to percolate and grow before you feel the effects. Its kind of like letting bread rise overnight -- the yeast need time to grow, so do bacteria.
How sick you get will depend on the type of infection and you ability to keep up with what you lose as vomit and diarrhea. If you are vomiting and cannot keep fluids down, you are going to get sicker than if you just have diarrhea.
Drink water or water with gatorade. Eat what you can. If you are having problems with vomiting, drink the water as small sips.