Clear out an area where you want to build the hearth, moving all furniture at least 36 inches from the stove position. Heating stoves need at least 18 inches of clearance in the front and 12 inches on the sides and back.
Place a sheet of fireproof asbestos millboard on the carpet, aligned with where you want to place the stove. This layer will protect the floor from any heat that might radiate through the hearth.
Add a 24-gauge sheet of steel on top of the millboard. You can cut the steel sheet yourself using a pair of aviation snips. Mark the steel with a permanent marker to match the size of the millboard.
Arrange bricks on top of the sheet metal in the pattern that fits the area best, doing a dry run without any mortar. Leave only about 1/8-inch space between the bricks.
Trim out the edge of the hearth with corner trim to anchor everything in place. Use 2 1/2-inch nails to hold the trim to the floor below the carpet.
Remove the bricks and add enough sand to make a 1-inch thick layer to cushion the bricks. Set the bricks back in place, settling them slightly in the sand. Pour more sand over the bricks and work it between the cracks with a brush to form a solid surface. Remove any excess sand.
Set the wood stove on top of the hearth, positioning the door at least 18 inches from the edge of the hearth.