You can also use a drywall saw to cut the drywall around obstacles. You can use either nails or screws to fasten drywall. Screws are stronger. Use one screw every 12 inches along the framing. There are special drywall screw guns which let you sink the screws a little below the surface.
Nails are probably easier to use.
Use two nails every 12 inches along the framing. Drywall hammers have a special head that sinks the nails below the surface. This makes it stronger. At the outside corners, attach metal corner bead. The joints of the drywall need to be taped and mudded.