Do not sand or scuff up anything.
Apply a coat of primer over the whole thing and allow to completely dry.
Use setting type 90, light weight joint compound, in small batches, to smooth out the imperfections. (It comes in a bag.)
Do not sand between coats - if you do, use a well wrung sponge, to remove excess dust, before applying another coat of mud.
Use the edge of a knife/trowel, to knock down any ridges/clumps, prior to additional coats of mud.
When you are satisfied, that you have a reasonably uniform surface, begin blending in the edges, with 120 grit drywall sandpaper. You can use 100 grit on thicker sections or ridges, but try to stick with the 120 as much as possible, following up with 120, if you use 100 on any spots. (Attach the sandpaper to a proper sanding pad/block - the bigger, the better.
Take your time, and start with the small spots first, gradually moving towards the bigger sections, as you build confidence, in your work.
When in doubt about drying times, there is nothing wrong with overnight - you'd be amazed what a fresh outlook in the morning, can add to the experience.
The wider the area, that you cover with mud, and subsequently blend into the surface below it - the flatter, the finished surface will appear, when painted.
If you have a portable shop light, or an old table lamp - put it opposite of you, close to the wall, while sanding, using the shadows, to even out the surface. (Turn off the decorative lamp, in the pictures too.)