Measure the outline of the chimney on the floor and mark it with a pencil. A standard brick is 8 inches long, 4 inches wide and 2 1/4 inches tall, and a standard mortar joint is 1/2 inch wide. Build your chimney with 8 bricks in a course so its outside dimensions are 21 by 21 inches and its inside dimensions are 13 by 13 inches. This allows you the space for a 12-by-12 inch chimney flue inside the brick chimney.
Lay a bed of mortar on the floor and create the first course of bricks by putting mortar on the end of a brick, seating it in the mortar bed by tapping it with the handle of your trowel, then adding another brick.
Build the clean-out door into the chimney so it is part of the second and third courses of bricks. The cleanout door is a metal frame with a small door set into it. It will allow you to clean out creosote and soot that falls to the bottom of the chimney when you clean it.
Cut a hole into the first piece of chimney flue so the hole will line up with the clean-out door when you put the flue into the chimney. Use a saw fit with a masonry blade to cut the flue. Insert it into the chimney after you have laid four or five courses of bricks. Constantly check both the flue pieces and the brick chimney with a 4-foot level to be sure they are perfectly vertical.
Build the brick chimney up to the level of the top of the first flue section.
Add another flue section by laying a thin bed or mortar onto the top edge of the first, then setting the second one carefully on top of it and checking that it's vertical.
Build the chimney up to the level where the thimble will be installed. The thimble is the round opening that the stovepipe goes into; it is usually installed about 6 feet above the floor.
Cut a hole in the flue piece that is even with the thimble so the thimble will fit into it. Install the flue piece, then the thimble, then build up the bricks around the thimble. Fill any spaces around the thimble with mortar. Reach inside the flue by putting your hand through the thimble and fill any gaps that exist between the thimble and the flue.
Add more courses of bricks until you have reached the desired height of the chimney.