I use charcoal because I love the difference in the flavor of charcoal grilled foods, but use whatever you're used to.
Be safe and don't have your grill up against your home or any out buildings unless you have a patio that has been specially built for an outdoor kitchen. Don't add lighter fluids or any other combustable to a fire that has already been lit. Don't add any styrofoam, plastic or cardboard (such as your plastic forks, plates, cups, etc.) with paint or coatings to the fire...these add toxic fumes to the environment and are cancerous to you. They'll also add disgusting chemical flavors to your food.
For charcoal: be sure to let all of the lighter fluid burn off before adding any foods to the grill. This is when the coals are all white. This is to ensure none of the lighter fluid fumes get cooked into your food ruining it. If you cook a lot of food at one time on the grill, like I do, get some wood charcoal or charcoal that doesn't have any added lighter fluid to use to add to your fire as the grill needs additional heat. For higher heat adjust the coals closer to the food and/or pile the coals deeper under the foods that require more heat. You can add different types of woods to add flavors while grilling. Soak the wood or chips in water for about 30 minutes before adding to the hot coals so it doesn't just burn away immediately.
To prepare the grilling surface, lightly wet a paper towel with olive oil and rub over the grilling grates. It's not a good idea to add oils by pouring or spraying during cooking due to flare ups. It's better to use oils and butters before adding the meat or vegetables to your grill. If your food is particularly fatty and you get flare-ups from the fat drippings, just keep a cup of water close and pour a bit on the fire to tame it down. Not so much that it will put your coals out.
Meats are usually cooked directly over the heat which will brown the outer layer searing in the juices and thus the flavors. You can also cook meats by using a smoker, a smoker works like an oven and adds the smoked flavors of the wood fire to the meat. Foods cook more slowly this way but it's a very nice way to cook outdoors.
Fish, like all other foods, can be cooked many ways. If your grill is very non-stick, like cast iron grilling grates that are well seasoned, you can cook directly on the grates. I used foil even when I had a nice non-stick cast iron grate grill, you're likely lose some fish in the fire that way. Foil can be used either as sealed packets, open packets or to cover the grilling surface. There is a new non-stick aluminum foil that when oiled is very nice for delicate fish. Also, fish can be cooked on wood planks that are finished with a sanded surface and the wood flavors infuse into the fish adding their delicious flavorings. Fish takes very little time to grill. If your vegetables take very long to cook, start them first. Prepare your fish while it is cooking on the grill then add the fish as it's almost ready to be removed from the grill.
I almost always cook many of my side dishes on my grill while cooking my meats or main dish. Our favorites are sugar snap peas, asparagus, mushrooms, corn on the cob...many favorites. Many are great with either butter or olive oil and some salt and pepper. You can add whatever type of additional seasonings you like. Do this before you get it to the grill...when you add seasonings over the grill the heat rising and burning then off can get them into your eyes...cheyenne pepper can be pretty scary if it gets into your eyes or sinuses this way!
Adding seasonings to olive oil or butters infuses the oil with the flavor and thus your meats. You can use them as rubs, marinades or add them right before cooking. If you need to make a sauce with oil or butter that will be poured over your meat because you are grilling directly on the surface...now is the time you can use that cast iron skillet to make extra. Some can be used on the meat while grilling but make more to pour over it. I'll add one of my favorites that I like for Tilapia as one of the first posts. It will be listed under Grilled Italian Tomato Mushroom Tilapia. Even the kids that come over to grill out LOVE this one!
You can also fix many different desserts while grilling. If your grill is large enough to have the coals on one side to heat the inside to 300-350 you can back a cake or cobbler on the opposite side. A Dutch Oven is on my list of wants right now.
I use my cast iron skillets with olive oil for many vegetables and they can be used for fish and meats as well. I mainly use them when I chop up things for salsas that I heat on the grill for meats. I have several of the very shallow ones that are smaller in size so they do not take up much space on my grilling surface. I got a set of 4 different types of skillets for $10 several years ago.
Let the hot coals burn off any foods that have stuck to the grilling grates. If your grill is adjustable you can move the heat closer to the grates to help this along. When the coals have entirely burned out, use a wire brush to scrub all of the remaining food off the grates. I love the special brush/scrapers that are sold for cleaning grates now. Make sure you get one that fits the curve of your grates. Some are more squared and some are more rounded.
I'm sure I'll add to this page as I think of more to add to it.