Scrubbing the interior of the fireplace is an important step. Not only is it supposed to get rid of stains, it reduces fire hazard.
First, you need to cover up any surrounding carpet or surfaces which you don’t want to get dirty. Lay a tarp on it, or some old magazines you’re going to throw away.
Second, you need to make a cleaning solution. The cleaning solution should be a mixture of warm water and bleach. Dip the scrub brush in the solution and start scrubbing away, especially at the places where soot and any creosote which hasn’t gone off yet. Make sure to scrub the floor of the fireplace too.