When I've written about making hamburger buns (and hot dog buns)in the past, I generally left out any sort of instructions for making the filling. Basic hamburgers are made with ground beef, which is seasoned and grilled over a relatively high heat, leaving a juicy inside and a patty with very slightly crisp edges.
The timing for grilling hamburgers varies so widely that I won't even offer suggestions as to how long you should cook you meat, but I will share a few tips on how to ensure that your burger is flavorful and juicy.

I have heard people say that they add everything from oatmeal and breadcrumbs to shredded vegetables to their hamburgers. While the vegetables are actually a pretty good idea, especially if you're trying to sneak a few more into a child's diet, oatmeal and breadcrumbs are for meatloaf - not hamburgers.
I saw this technique on Paula Deen's show well over a year ago and it works beautifully. Simply add a bit of water to your (lean) ground beef, just a tablespoon or two per pound, and some salt and pepper before mixing it up. Once it is well blended, shape the meat into balls, making twice as many balls as the patties you want (4 patties = 8 balls).
Place all the balls on a plate and season them with a bit more salt and pepper. Place one ball on top of another and squish them into a flat patty. Because the meat will shrink and get a bit thicker as it cooks, it is wise to make them larger and thinner than you want them to be. I estimate the size using one of my buns to make sure that they'll fit.
Once all the patties are shaped, you can put them on the grill, or even freeze them for later use. It really does seem to keep the burgers moist, and the extra seasoning (feel free to use spices other than salt and pepper) in the center improves the flavor of the burger.