Dig out an 8-inch deep trench. The trench can be any dimensions you like, but it should measure in length and width in multiples of the size of your concrete blocks.
Lay the first row of blocks inside the trench. As you place them in the trench, make sure that they are flush with the surface of the ground. If they are too deep, add sand beneath the ones that are not level bringing them to flush, and if they aren't deep enough, dig out a little more dirt underneath the ones that are sticking up. This is your foundation.
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.
Finish off the foundation with bricks and sand. Lay down your fire bricks inside of the first row of blocks. Cover the bricks with sand and fill in all cracks between them. This will be the foundation for all of your fires.
Enclose the back and sides of the pit. Build up your concrete blocks to about 40 inches high, leaving the front open. You are not using mortar here, only the weight of the bricks, so they will have to be precisely put in place.
Make the mount for your grate. On the inside of your pit, stack concrete blocks three high on each side, and make sure they go all the way to the back. This will be where your grate sets upon.
Set the grate in place. If you want a sturdy grate, stack two concrete blocks end to end on each side on top of the grate. This will hold it down securely. If you plane on taking it off and cleaning it regularly, you may want to skip this and just lay it on top of the blocks.