Homemade pizza is one of those flexible favorites; it's great for an appetizer party if there aren't too many people around - each little pie is enough for a person, but it's great fun to make them sequentially with different toppings and everybody trying a slice each time.
This dough recipe is straight from Mark Bittman's recipe for "Pan-Fried Pizza" feature, with only a couple of caveats:
1. You can also bake this in the oven. Crank up the heat (pretty much as high as it can go), and if put whatever you're baking it on in the oven for a good ten minutes or more first. You want it going onto a hot surface as well as in a hot oven. Also, par-baking it a little first (so it's a little bit cooked on top) will help the crust hold up to the tomato sauce and not get too soggy.
2. The rising times here are approximate, and more pretty much never hurts. You can always make pizza dough ahead by a day, and let it rise in the refrigerator overnight - the longer and cooler the rise the denser and chewier the dough.
Other than that - go to town! Everybody knows already how they like their pizza best.
2 cups all-purpose or bread flour, more as needed
1/2 c. + warm water
3/4 teaspoon instant yeast
1 teaspoon coarse salt
3 tablespoons extra virgin olive oil, more for cooking
Bittman suggests a food processor for this; I suggest your hands. Combine the first 4 ingredients plus 2 tablespoons of olive oil in a large bowl and work it together with your hands. Kneading for three or four minutes at this stage is a good idea, working it around in the bottom of the bowl and adding more water if necessary so that the dough is only slightly sticky to the touch; the kneading will make it more springy. Coat the dough ball very lightly in olive oil and cover the bowl with plastic wrap - now you can either let it rise for a couple hours on the countertop or for longer in the fridge.
About the water
Getting the water temperature right when working with yeast is pretty important; I'm no expert but the target temperature for instant yeast is somewhere around 100 or 105 degrees. The easiest way to measure this is to stick your finger in it; if the water feels just barely warm, you're in the right range (because your body temperature is about 98.6 degrees). Lips or the inside of your wrist would also be good thermometer-zones (as they are for baby bottles). You can also use an actual thermometer, of course.
After the (first) rise
Divide the (now hopefully larger) dough ball into four pieces; make them into balls by sort of tucking the bottom under and pinching. Dust these with flour and let them rise again for another 1/2 hour or so under a damp towel (or even return to the fridge). The point is, they need to be room temperature when you go to pull them.
Dealing with dough
Stretching the dough can be a bit tricky; it also has a tendency to spring back, so I use a two-round approach. The first time, squash the ball and then flatten into a disk with your fingertips and by pulling slightly (holding the dough in the air). Then you can put it back on the counter and plant the heel of one hand on the disk while massaging the other side outward with your fingertips, rotating the dough a little at a time. You don't generally want to roll it, but you can if you get frustrated. It takes practice.
Usually after the first round of stretching, I kind of stick the dough to the counter and let it rest for another few minutes under a damp towel, then stretch it out again - the interim "rise" makes it spring back much less.
If you're pan-frying, preheat your skillet to medium heat and put a very little bit of oil in it; you don't want really greasy pizza. Cook the dough for four or five minutes until it's reached your preferred doneness, then flip, add your toppings, and cover the pan (so the toppings warm and melt). That's it! For the oven it's much the same, but you'll want to par-bake the dough a little longer. Naturally - top as you please!