It is usually inappropriate to join a table already occupied by other diners, even if it has unused seats; Americans prefer this degree of privacy when they eat. Exceptions are cafeteria-style eateries with long tables, and at crowded informal eateries and cafes you may have success asking a stranger if you can share the table they're sitting at. Striking up a conversation in this situation may or may not be welcome, however.
Table manners, while varying greatly, are typically European influenced. Slurping or making other noises while eating are considered rude, as is loud conversation (including phone calls). It is fairly common to wait until everybody at your table has been served before eating. You should lay cloth napkins across your lap; you can do the same with paper napkins, or keep them on the table. Offense isn't taken if you don't finish your meal, and most restaurants will package the remainder to take with you, or provide a box for you to do this yourself (sometimes euphemistically called a "doggy bag", implying that the leftovers are for your pet). If you want to do this, ask the server to get the remainder "to go"; this term will be almost universally understood, and will not cause any embarrassment. Some restaurants offer an "all-you-can-eat" buffet or other service; taking home portions from such a meal is either not allowed, or carries an additional fee.
Many fast food items (sandwiches, burgers, pizza, tacos, etc) are designed to be eaten by hand (so-called "finger food"); a few foods are almost always eaten by hand (french fries, barbecue, chicken on the bone) even at moderately nice restaurants. If unsure, eating finger food with a fork and knife probably won't offend anyone; eating fork-and-knife food by hand might, as it's considered "uncivilized" and rude.
If you're dining at a restaurant and can't finish what's on your plate (which often happens to visitors unaccustomed to the giant portion sizes prevalent throughout the USA), always ask for it to be "wrapped to go" or for a "doggie bag," even if you have no intention of eating it later. If you don't want to eat it later then discreetly throw it away or give it to a homeless person after you've left the restaurant. Leaving food on your plate is considered wasteful and a universal sign that you weren't happy with your meal.
When invited to a meal in a private home it is considered polite for a guest to ask if they can bring anything for the meal, such a dessert, a side dish, or for an outdoor barbecue, something useful like ice or plastic cups or plates. The host will usually refuse except among very close friends, but it is nonetheless considered good manners to bring along a small gift for the host. A bottle of wine, box of candies or fresh cut flowers are most common. Gifts of cash, prepared ready-to-serve foods, or very personal items (e.g. toiletries) are not appropriate.
An exception is the potluck meal, where each guest (or group/family) must bring a food dish to share with everyone; these shared dishes make up the entire meal. Usually dishes are grouped (e.g., salads, main dishes or casseroles, side dishes, desserts); you should ask the host if they want you to bring something in particular. Ideal dishes for a potluck should be served from a large pot, dish, or bowl, and would be spooned or forked on to diners' plates—hence the emphasis on salads, casseroles, and spoonable side dishes.