Check the wall before patching
If the drywall feels damp or soft, has a stain that keeps returning, or was damaged by an active leak, fix and dry the source first. Look out for plumbing or wiring behind the wall; do not cut into an area unless you know what is there. Large water-damaged or moldy sections need a proper assessment.
For a small dent or nail hole
Remove loose paper and dust. Press suitable patching or joint compound into the opening with a putty knife and smooth the edges. Let it dry fully according to the product label. Add a thin second coat if needed, then lightly sand after it dries.
For a larger hole
A larger opening needs a supported patch or repair panel rather than a thick plug of compound. Fit the patch to sound wall material, secure it using the patch system instructions, tape or reinforce the joints as directed, and feather successive thin coats beyond the seam. USG publishes repair methods for different hole sizes.
Finish the surface
Use dust control and protect nearby furnishings while sanding. Wipe away dust, prime the repaired area, and then paint. Skipping primer can leave a visible change in sheen even if the patch feels smooth. Texture matching can take extra work on an older wall.
Technical reference: USG: drywall repair how-to guides ↗