Hang as many full drywall panels as possible, to cover walls without cutting. Fasten panels with drywall screws, driven in with a screw gun until the tops make a dimple in the drywall, but do not break the paper facing. Space screws at every stud, 16 inches apart, and about every 18 inches vertically. Install all ceiling panels first so wall panels will support the edges. Set wall panels either horizontally or vertically.
Cut drywall to fit odd spaces with a straightedge and a utility knife. Score the drywall along the straight line with the knife and snap it in two against the straightedge. Make the cuts as smooth as possible. Use a drywall rasp to smooth rough edges where drywall was snapped apart. Cut panels with a drywall saw or jigsaw as an alternative.
Overlap panels on outside corners, so one edge extends past the edge of the abutting panel. Put any cut edge to the inside. Do the same on inside corners, with one panel to the inside edge and the next adjoining the face of that panel. Use the same technique on angled corners. Run one panel to the end of the corner and set the adjoining panel with its edge against the face of that panel.
Use paper tape to seal unusual corners; it is easier to manipulate to conform to the angle than fiberglass mesh tape. Spread joint compound on both sides of the angled seam with a 2-inch drywall knife. Fold the paper tape in the middle and put the fold into or onto the angled corner, then secure the edges with another layer of compound. Let that dry and finish with a second coat just like on any other taped seam on drywall.
Apply that technique to any joint or seam other than a corner such as where a vaulted ceiling panel connects to a vertical wall at other than 90 degrees. Seal those angles like any other seam, with the fold of the paper tape in the gap where the panels meet and the tape edges flush on the two adjoining panels.