Griddle Size: The right griddle for you needs to give you the space you want both in griddle space as well as the grill space. You can get a griddle that covers the entire grill area or a smaller griddle that leaves you with room to grill as well. If you have a small grill you'll probably want a full size griddle but if you have a large grill surface you might want to leave some space for grilling while you have the griddle on the grill. You can generally find griddles in many different shapes and sizes. Have a kettle style charcoal grill? There are round griddles to fit it.
Charcoal Griddles: On a charcoal grill you need to make sure that the griddle you get allows for sufficient air flow. It should not fit the grill surface too closely otherwise the fire will be starved for oxygen due to low airflow. Otherwise you can use a griddle on a charcoal grill as easily as you would a gas grill. One thing to think about however is hot and cool zones. Do you want to have a very hot section of you griddle and a medium warm section? If so you will need to bank more coals on one side of your charcoal grill than the other. With a multi-burner gas grill you can have one burner on high and the other on medium to create these different cooking zones.
Griddle Secrets: Outdoor cooking on a griddle is very easy. Having the different cooking zones is a good idea so that you can more foods around as they get cooked. You will also want to make sure that you have some kind of oil or butter handy. Unless you are using a nonstick griddle you need to cook with oil, cooking spray or butter to keep foods from sticking. Be warned when using cooking sprays near an open flame. Cooking sprays can be very flammable and so either avoid them all together or make sure you are extremely careful.
Griddle Safety: It is a good idea to have an oven mitt or similar item available when grilling with a griddle. They tend to move around on you and you might need to quickly get them back in place. A good sized spatula is also a must. You should also be prepared to deal with excess grease when using a griddle. If, for instance, you cook up a lot of bacon you need to make sure that bacon grease has someplace to go. Grease falling into the open flame of a grill is not a good thing. Grease fires can be a big hazard so make sure you don't end up with an excess of grease on your griddle. Either keep it drained away or plan on foods that soak up grease.