Sanding the drywall is equally as important as applying mud. Sanding require basic skill but it must done right. Sanding too much can create a creator in the wall and too less can leave convex shape bumps. You will need two equipments: One is a hand sander and the other is a 180 grit sandpaper.
First use the hand sander and go over the dry compound using short stroke. Make sure to sand gently to prevent dry compound from falling off. Go around the edges and work your way in until the patch is nice and flush with the wall. The goal here is to have smooth edges so the patch won’t show before and after painting.
Once you have completed sanding. Use a broom and sweep the wall using long stroke. Make sure to not sweep all over the place. You may want to sweep the ceiling, wall, corner, and the floor. After sweeping use a wet rag and go over the wall. The reason to sweep the dust is because primer will not stick to dust and ti will be counter productive.