Remove the back of the kindle.

The back is glued in the middle to the stainless steel battery cover with double sided tape, and attached with 2 tabs at each end. The top and bottom tabs slide into the frame, so if you pull too hard they might break. Once you have unclipped, use a hot air gun on moderate temperature to help release the double sided adhesive.

Watch out for static electricity, it might destroy your device. Discharge before you start by holding a radiator or using a strap.

Start with opening the back at the sides. Push your knife or tweezers in a bit deeper at the middle and twist them to push the glued cover part from the frame. Don't do this near the side buttons as you might cut the buttons' ribbon cable.

See this video from 0:33 to 2:00. Do not follow it any further as you don't need every step from this video to replace the screen!