How to grill hamburger patties on a charcoal grill?

I admit, I am a grill rookie. I'm trying to grill burgers on the grill. I have a Weber charcoal kettle grill. Last night, I grilled some burgers. They turned out so so. The problem was that some of the patties fell apart. I know that you should only flip once, but here in lies the problem, when the grease and juice from the patties hit the charcoal briquettes, this caused flames to rise and the patties got way to charred on the outside. I like my burgers medium with nice slight grill marks. In essence, how do I keep the patties in tact and keep the flames to a minimum so they cook nicely without burning? Am I using to much charcoal, is the grill grate causing the patties to stick? Any advise, please share.