Roll Gently on Textured Ceilings
Painting textured ceilings is a bit of a crapshoot. If the texture has been painted over already, it's probably safe to paint again. If the texture has never been painted, there's a risk the water in the paint could loosen the texture, causing it to fall off in sheets. A lot depends on the quality of the texturing job. If you have a closet or other inconspicuous area, do a test by rolling on some paint to see what happens. If the texture loosens, painting over the larger ceiling is risky.
If possible, spray on the paint—it's less likely to loosen the texture than rolling. But spraying in an occupied house is usually impractical. The best tip for rolling on paint is to avoid overworking the paint. Just roll the paint on and leave it. Don't go back and forth with the roller, as this is likely to pull the texture from the ceiling. If the ceiling needs another coat of paint, wait for the first coat to dry completely. Then roll another coat perpendicular to the first one using the same careful technique.