Apply painter's tape to the baseboards, windows, ceiling and adjacent wall joints. This small step will save time.
Use a two-inch angled paintbrush to paint the edges of the wall first. This is known as cutting in. The roller cannot reach these areas. Use adequate amounts of paint, but if it doesn't cover the original color fully, don't overdo it. It's better to do another coat. Work your way from the higher areas at the ceiling downward.
Cover the rest of the wall using a roller. Work in small sections. Three feet square is a good size. Again, work from top to bottom. Do not stop midway. This can leave a drying line.
Allow the paint to dry.
Determine if you need a second coat. It can be difficult to tell ahead of time, because the coverage power of the paint depends on pigment color and load. In general, darker and more expensive paint (which are usually highly pigmented) will do a better job.