Although pasta comes in numerous shapes and sizes, assorted ingredients, and from countries all over the globe, there are truly only four basic kinds: dried, fresh, frozen, and canned. Here we will discuss only Italian pasta, and we will not even consider the canned.

DRIED PASTA: Semolina and water are worked into a stiff paste (hence the Italian pasta). This is then rolled, extruded, stamped, cut and/or hand-shaped, and air or oven dried. Colorful–often fanciful–names describe these shapes:
   Alphabets (small letters) are usually used in soups - children's favorite
    Capellini (angel hair - fine hairs) works best with thin and delicate sauces
    Cavatelli (small hollow shells or bullets) does well in soups, salads and cheese sauces
    Conchiglie (conch shells) is also good in soups, salads and cheese sauces
    Ditalini (little thimbles) can be used almost any way
    Farfalle (bow ties - butterflies   ) is good with most sauces, salads and soups
    Fettuccini (small ribbons) is perfect for heavier meat, cheese, and tomato sauces
    Fusilli (twisted spaghetti) goes well with almost any sauce
    Lasagna (cooking pot or chamber pot?) is a broad, flat noodle used in casseroles
    Linguini (little tongues) goes with most sauces, especially clam sauce
    Macaroni (a dumpling, a fop ) goes with most sauces, and is good baked
    Manicotti (hand muffs) is stuffed and baked
    Mostaccioli (little mustaches) is like large penne and may be treated the same
    Orzo (barley) can be used in soups, pilaf, or in place of rice
    Penne (quills) takes most sauces, and is good baked or in salads
    Ravioli (dumplings) are usually fresh or frozen due to the stuffing
    Rigatoni (lined) is a large, curved, ridged macaroni that can be treated like penne
    Rotini (twists) are best with chunky sauces
    Jumbo shells (large conchiglie) are best stuffed, covered in sauce and baked
    Spaghetti (small cord) will fit with almost all sauces
    Vermicelli (little worms) between spaghetti and capellini in size, will take most sauces
    Ziti (bridegrooms - for apparent reasons) takes chunky sauces and is often baked

Dried pasta usually calls for oil-based sauces.

FRESH PASTA: This is mostly made of white flour, egg yolks and water. As with dried pasta, other ingredients are sometimes added to give added flavor and color: e.g. tomato paste, spinach, red peppers, herbs or squid ink. It usually takes sauces based on butter or cream.

FROZEN PASTA: Often this is stuffed pasta such as lasagna, ravioli or manicotti - or gnocchi, which is traditionally made from potatoes. I never use frozen pasta, so you're on your own. Follow manufacturers' instructions on the package, but not too carefully - they are often wrong.

Something all pasta has in common is a need to cook in large quantities of salted boiling water. NO OIL IS NECESSARY. If there is enough water, and if the pasta is stirred until the water returns to a boil then occasionally stirred thereafter, it will not stick together. Nor must pasta be overcooked. A minute or so before the suggested cooking time is up, bite into a piece to test it. It should be al dente (to the tooth), cooked just to the point where it is barely done. It will continue to cook after it is drained. DO NOT RINSE.

Due to differences in thickness and shape and ingredients, cooking time widely varies. Whereas it is obvious that capellini will cook faster than rigatoni, and that fresh pasta will cook in less time than dried, it is not readily apparent how great that time difference is:

I find that thin DRIED PASTA should be tested for doneness after about six to seven minutes, fatter noodles after eight or nine. Homemade FRESH PASTA generally takes three minutes, commercially manufactured pasta takes four. In some recipes the pasta will be left undercooked by about a minute, drained, then added to the sauce to finish cooking. Remember, you can always cook the pasta longer, but once it is overdone there is nothing you can do but start over - or eat mush. Test early. Experience will soon guide you.

When properly done, pasta will have a rough surface. This allows the sauce to cling. It helps the pasta cling to your fork, too.  Pasta also has more flavor when it is not overcooked. And as the Italians well know, pasta - not the sauce - is king.