Sizing: You can grill any size mushroom, but you will need to use different equipment and cooking methods in order to accomplish this. Large portabella mushrooms (perfect as a hamburger patty can be grilled as is; right on the grate, as with other types of mushrooms that will remain big enough not to slip through your cooking grate. Remember that they can lose as much as 50% of their size as they cook. Smaller mushrooms can simply be run onto skewers for easy control on the grill. Remember to be gentle with them as they can break easily and use tongs for turning, not forks, or spatulas.
Preparing: Many people will tell you that you shouldn’t wash your mushrooms in water. Mushrooms should be gently brushed of any remaining dirt or debris. Of course, most restaurants, even the fancy ones, rinse off their mushrooms to get them clean. Individually brushing them off should only be attempted if you have a lot of free time. As for the stems, just trim off the dry end, unless the stem is going to get in your way (like for a portabella mushroom burger). If you do rinse off the mushrooms before cooking do it right before they hit the grill.
Flavoring: You can marinate mushrooms for up to a day or so in advance. Mushrooms are very forgiving that way and since they are going to be clean of bacteria you don’t have to worry about the marinade becoming contaminated. So you can marinate well in advance, but I find that mushrooms can be seasoned right on the grill. Take a small amount of olive oil, add garlic, salt and other seasonings and brush (or mop) this onto the mushrooms as you cook them. If you are preparing mushrooms as a side dish, season them with the same mixture that you have used for the main dish. This provides complimentary flavors that ties the meal together.