Arrange cinderblocks as shown, after knocking vent holes at the bottom of one (see photos). The grill plate came from Walmart ($10 new, got mine from rusted out old grill after much use). The "chimney" works backwards, as a cool air induction vent when the coals are going well. A couple 12v computer fans can be added with a battery behind the bricks, to speed up heating or cooking. I use a $3 110v desktop fan aimed down into the brick.
You can also get free grates from discarded ovens. They can be hack sawed or sawzall'ed to a smaller size, or you can just lay one on the bricks so it balances well. You can get a super nice cast iron one for $30 from Walmart. You can find 12v computer fans in junked appliances and computers. Hobby batteries work, or an older car battery can easily run the fans even if too weak to use for an auto (like one with a dead cell or several years old). It's not even necessary but does help speed up heating from a cold pit to hot bbq.
Add some black clay to the bottom of the pit, about 2" deep. This helps insulate the ground and keep the charcoals put. You can simply hose down the coals to extinguish the grill, and let the sun dry them out. Add some fresh ones next time you cook. The used coals are still fine and will light after you get your new ones going normally (lighter fluid on a pyramid of coals, then spread them out when burning well).
When the pit is too full or if sauce and food etc spills on the coals, just move the front brick and shovel out what is unneeded after all is well extinguished.
You can add some lava rocks among the coals to promote even heating and economize on your cost of charcoal briquets.
I get a lot of free charcoals from the park, left from when people are done with their bbq. I just sift the coals from the ashes and take home the coals.
If you want to be fancy, the bricks can be painted (outside of bricks) with red rust colored primer or whatever color you want. It won't burn up because the heat is in the middle of the grill.