Apply painter's tape to any trim or fixtures that you don't want painted.
Prime the drywall's edges with a general purpose primer and a paintbrush. This is referred to as "cutting in," and it leads to a better-looking finish for primer and paint when compared to using a roller for the entire surface.
Prime the main surfaces with a roller. Wait for the primer to dry.
Paint the primed edges with a paintbrush and interior latex paint. A latex paint with a flat or eggshell finish is typical of drywall, but you can use paint with a semi-gloss or high-gloss finish if you prefer.
Paint the main surfaces with latex paint and a roller. Roll the paint on in parallel strokes to prevent unwanted roller marks.
Apply a second coat of paint if needed after the base coat dries. Fresh drywall will often cover nicely in just one coat, but sometimes a second layer of paint is necessary.
Remove the painter's tape once the final coat dries.