Assuming everything is taped and floated and ready for paint;
1) Sweep and vacuum to remove all of the dust, especially next to the walls.
2) Knock off any remaining dust and apply wallboard primer (PVA), if spraying use a 1/2 or 3/4 inch roller and back-roll the primer.
3) Now paint in same manner as the priming. Back-rolling the first coat might be need if there is a heavy texture.
That's it. If the ceilings are a different color or sheen than the walls then spray those and brush/roll the walls.