The "Law" in italy isn't that restrictive.
It basically states that if you want to put on a menu something called:
Pizza Napolitana D.O.C.
it needs to be certified as having:
A) A crust made from wheat flour, water, olive oil and yeast, of a certain size and thickness.
B) cherry tomatoes (I could be wrong about this) on the toppings
C) Mozzarella di Bufala (Mozzarella made from water buffalo milk)
D) Baked in a wood-fired oven.
Nobody believes this is the _only_ pizza out there. It is, however, the original, and, if I might say so, damn tasty.
Chairboy is right about texture and flavors. Many fast-food pizza places in the US love to emphasize the cheap parts of pizza making: the toppings, for example, at the expense of the others.
Central to the pizza experience are a series of contrasts:
In terms of flavors:
First there's the classic acid-fat tension between the cheese and the sauce. Acid-fat mixtures are what make marinades tangy, and salad dressings tasty.
This is where a practically raw tomato sauce comes in handy. Cooking tomatoes reduces their flavor complexity considerably. For best results, I use garden-fresh tomatoes, run them through a vegetable mill, and spike them with Huy Fong sriracha, garlic, salt, pepper, and some chopped fresh basil.
That gives you a nice, bright sauce, full of flavor and youth and brassy tones.
Otherwise, just get a can of crushed tomatoes and cook it down with garlic, some red wine and sriracha -- the tones will be darker, of course.
Many pizzerias cheat by adding sugar to the sauce, since people tend to mistake sweetness for goodness.
The cheese needs to be fatty; it also needs to be fresh. Most of the "mozzarella" sold in the US is this part-skim crap that's not worthy of the name. While Mozzarella di Bufala is ideal (it has a higher fat content than regular Mozz, so it's richer and creamier), I find that regular fresh mozzarella (the kind they sell in balls floating in water) does pretty darn well. The key is the high moisture. When it cooks up, the mozzarella should be roughly the same consistency as the sauce, so that, instead of having distinct layers of cheeze and sauce, the one blends into the other (of course, the proteiny stringiness of the cheese and its higher heat retention make it immediately distinguishable in the mouth from the boiling acidity of the tomatoes).
I also like to sprinkle some pecorino romano or even parmigiano reggiano on the top to give it a certain saltiness.
The preparation of the dough likewise needs a lot of consideration. Some fast food pizzerias use chemical leavening agents (such as baking soda) because they're easier to train 16-year-olds how to use than proper yeast. This is heresy.
Pizza dough is a bread, not a pie crust. The distinction is important. Pie crusts get their flakiness through care being taken not to develop the gluten in the dough to long protein strands. With a pizza, we want those proteins. This crust has to stand firm underneath the weight of the toppings; and we're counting on it to provide a dry and crispy counterpart to the wet and chewy sauce and cheese.
So I look for a flour with a somewhat elevated gluten content; also be sure to pick flour that has a predictable gluten level (Pillsbury and Gold Medal, for example, tend to vary from bag to bag). Some will pick bread flours for this; I usually go with King Arthur general purpose unbleached white flour. Its gluten level is higher than the normal GP flours, and it's predictable.
Alternatively, you can buy a box of wheat gluten and mix it in.
Anyway, be sure to use good filtered water, and live yeast. My ratios of water to flour tend around the 2.5:1 area. Throw in lots of extra virgin olive oil too. That'll help it bake up crisp.
I usually go for two risings, though I'm rarely at the proper 110 degrees F.
How to bake the pizza matters a helluva lot too. Many pizzerias use abominations such as conveyer ovens, which produce a flaccid and unimpressive crust. Ideally, you want a wood-burning stove, but if you're like me, you're not that much of a snob that you'll go out and buy one. Instead, I use a baking stone. These have become somewhat popular lately, but unfortunately most are cheap and thin rocks that break easily. If you can, get one that's at least a half-inch thick, if not more.
The idea behind the baking stone is that the rock gets hot first (hence you run the oven with the rock in it for 30-45 minutes before the pizza goes on), and the bread is placed on the rock instead of a metal pan. Since metal's an excellent conductor, the surface of the crust is actually cooler than the oven, and the crust doesn't get so crisp as when it's sitting on a rock, a massive heat sink. Moreover, the porosity of the rock absorbs some of the moisture from the dough, giving a nice thick crust on the bottom of the pizza.
I usually run my oven at 450F, but the exact temperature depends on environmental circumstances, as well as the moisture of the ingredients themselves (if you get a really wet cheese, you'll have to go pretty darn hot). Of course, a proper pizzeria with the wood stove runs very hot indeed.
Oh yeah, a few other things: roll the dough out and slap it on a wooden peel that's been liberally coated with corn meal. Cornmeal in the oven doesn't burn like flour does, and it adds a distinctive taste to the pizza.
A word about toppings: make them good, and pick them welll. Again, it's an overall experience, not a competition to see how much crap we can pile up. Also, some will need to be put on towards the end so they don't fully cook (As in the famous prosciutto crudo (aka "speck") and arugula mix -- put the arugula on at the last minute).
Some other combinations I love;
pepperoni: make sure it's cut thick, and stuck under the cheese, otherwise it comes out tasting like ash. Onions or pepperoncini go good on this too.
quality anchovies (not the sawdust variety), capers, onions and extra pecorino (umame baby) -- the italians would object that fish and cheese is heresy, but it's good here.
Artichoke hearts (not-marinated, I found out) and mushrooms. Slip in some gorgonzola dolce to finish this one off.
Merguez and Grilled Eggplant, with Argan oil drizzled on the top is great as well.
As for accompaniments: beer is good; the italians prefer white wine, going for the hot/cold effect; much of the rest of hte world recommends a light red.
and avoid trendy pizza folks who do obscene things to their pizzas. respect tradition, but enjoy your meal.