The final stretch is where good substrate work either pays off or gets undone. The goal is a surface that's flat, properly textured if your wall has a texture, and primed before paint touches it.
Sanding and Texture Matching
Sand with a fine-grit sponge using gentle pressure, working in circles to feather the edges into the surrounding wall. The sponge should glide — if you're pushing hard enough to leave grooves, you've mudded too thick. Stop sanding the moment the patch feels flush with the wall, and absolutely stop before you start tearing the paper face of the surrounding drywall. A fuzzy, torn surface from over-aggressive sanding is one of the few patch problems that primer can't fully hide.
If your wall has a texture — orange peel, knockdown, or, on older ceilings, popcorn — match it before primer. For orange peel, an aerosol orange peel spray applied in light passes from about 18 inches away can work well; many DIY-ers also have luck loading a thick-nap roller with thinned premixed compound and rolling the patch lightly. For knockdown, spray the texture, wait a few minutes for it to firm up but not fully set, then drag a wide knife flat across it to flatten the peaks. Practise on a scrap of cardboard first; texture spray cans don't behave intuitively, and one heavy pass on the wall is hard to undo.
Priming and Painting
Once the patch is smooth and textured, prime. According to Gypsum Association guidance, drywall primer is formulated to fill the pores in joint compound and equalize the suction difference between the compound and the surrounding gypsum face paper. Without primer, paint applied directly to bare compound is partly absorbed into the patch, leaving a duller, differently-textured sheen than the rest of the wall — the trade calls this "flashing," and it's the unmistakable signature of a skipped step. A standard PVA drywall primer or a high-build drywall primer will solve it. Roll the primer on with the same nap you'll use for paint, let it dry fully, then paint as usual. If the wall colour is dark or the patch sits in critical light, two coats of paint will give you the cleanest match.