Check your plans with your local fire department before you build.They can tell you about rules or laws governing where exactly a barbeque like this should be, as well as any permits required to build one.
Dig out an 8-inch deep trench. You can use any length, but it's best to conform to dimensions in multiples of the measurements of your concrete blocks. When you are done, the trench will be the outline of your BBQ pit.
Lay the first row of blocks inside the trench. Make sure they are flush with the surface of the ground. Straighten them off using the level. If the blocks are too deep, add sand, and if they are not deep enough, dig out a little more dirt.
Enclose the foundation area. Put your first row of blocks down over the foundation going all the way around, even across the front. Doing this will enclose the entire foundation area for burning. The blocks should stack easily and you will not need cement to hold them in place.
Create the floor of the pit. Lay down your fire bricks inside of the first row of blocks. Cover with sand and fill in all cracks between them.
Build up the walls of the pit. Stack your concrete blocks to about 40 inches high, leaving the front open. Since no mortar is being used, they will have to be put in place precisely. This is not difficult. You just have to keep on eye on placement so they create a smooth wall surface.
Set up your grate inside the pit. On the inside the pit, stack concrete blocks three high on each side, and make sure they go all the way to the back. This will be the stand that your grate sets upon. Place your grate on top of the stacked inside blocks, and decide what will be first on the menu.