If you are in St. Louis, and looking for the Most Excellent Burger...
(not listed in order of preference, just in order that I'm typing 'em)
Seamus McDaniels, in the Dogtown district, just south of Forest Park. Huge burger, nicely crafted, and they have Guinness on tap.
O'Connell's Pub - South of Barnes on Kingshighway - consistently voted "best burger" in the local alternative rag.
Blueberry Hill - Delmar Loop area - in a fight with O'Connell's as to who gets the listing that year.
There's also a Fuddrucker's in town. Meh.
Going west, toward Columbia, there's an outfit called 54 Grill or somesuch that isn't bad.
To cook a burger... Start with the cheap stuff. NOT the "nice lean" stuff.
BIG patties, suitably thick.
Get your charcoal going, nice and hot, and sear the outsides, just long enough to somewhat sear 'em... Move the burgers to a different, cooler (somewhat...) part of the grill, and put the lid on. Oh, and there is ONLY one kind of grill - the Weber. Let 'em cook/smoke until they are your desired state of doneness. Put 'em on nice kaiser rolls (not the buns from the bread aisle), and enjoy.