Measure the dimensions of your firebox. Make sure you have enough room to build the firebox and that the floor is level.
Outline the dimensions of the firebox on the floor using a marker. Determine how high you want the floor of the firebox to be and select an appropriate foundation material. A thin sheet of cement may be preferable to blocks. Use molding or cement to secure the foundation into place on the floor.
Cover the foundation with a layer of firebricks, dipping the bricks in the mix to coat the bottom and sides of each bricks. Use a hammer to tap each brick firmly into place.
Build the wall of the firebox starting at the back. It should be at least 8 inches thick from the surface exposed to direct flame. Dip each brick in the mortar and put it tightly into place.
Work your way forward on both sides, interlacing (staggering) each successive layer on top of the previous one. If your brick is 4 inches wide, lay two interlocking rows side by side. Place bricks across the wall in a staggered fashion to connect the walls and add strength.
Check your work using a level to make sure everything is straight. Cut half-bricks using the brick saw when you need a half-brick to finish a row. Ensure each cut is exact so the bricks fit tightly together, preventing gaps that would allow flame to get through
Finish the firebox by completing the walls to the top. Depending on your design, you can now continue building the rest of the fireplace, including draft, chimney and so on.