Have you ever grilled a pizza? And I don't mean getting one of those grilled pizza pans from Papa Murphy's; I mean actually putting the crust on your grill and actually cooking the pizza on the grill. If not, you should. I know, I know, the thought of putting raw pizza dough directly on the grill is scary, but you can do it. I'll be there with you.
Grilling a pizza is a quick process, so before you begin, make sure you have all your ingredients ready to go and outside at the grillside. So, if you're using veggies, get those chopped up and on a platter or bowl. If you're using toppings, get those ready too. If you're making sauce, get that ready, too. Having this all ready and at the grill before you get started cooking it will help you tremendously.
Heat your grill to 350 degrees.
Roll out your favorite pizza crust on a lightly floured surface. Don't worry about it being particularly pretty or organized. What matters is that it's about 1/4-1/2" thick. Put that crust on the back of a cookie sheet (or a pizza peel, if you have one) and take it out to the grill. You can use any crust you want, but I used this one from Mario Batali and it worked great.
Make sure the grate on your grill is well-oiled. Put the pizza directly on top of the grill. Trust me - it won't fall through. Cook for about a minute or two and then flip it over. Immediately after you flip, add your toppings. You should do this quickly to make sure your pizza doesn't burn.
After your toppings are added, cook for another minute or two. Remove from the grill. Let sit for a couple minutes before cutting. Your pizza will have a nice grill flavor, and will also have a great crunch like woodfire pizzas.