Paint the corners and edges of the ceiling with a paint trim pad first. Some people make the mistake of painting these small areas with a paint brush and then using a roller on the rest of the ceiling, which causes lap marks.
Load your paint roller lightly. Too much paint will cause smudges and lap marks as well.
Paint a strip across a small section of the ceiling.
Roll back across the outer edge of this strip so that you even out the edge of the first swipe while applying paint to a new section. Repeat this process over small areas of the ceiling until you have covered the entire ceiling.
Keep the temperature in the room at a comfortable level. If the temperature gets too high, the paint will dry quickly and you may see lap marks.