A brown ring on the ceiling means water got somewhere it shouldn't. The stain is the symptom. Here's the order to deal with it.
1. Find and stop the source
Look at what's above the stain: a bathroom, a tub or shower, a radiator, an upstairs unit, or the roof. A plumber or roofer may need to fix the source. Painting over an active leak just hides the next stain for a few weeks.
2. Check the drywall
Press gently near the stain. If it's soft, crumbly or sagging, that section needs to come out. If it's bulging with water, keep people and furniture out from under it and get help right away.
3. Let it dry
Wet drywall and the framing behind it need time to dry out before any repair. Opening the damaged area helps it dry and shows how far the water went.
4. Repair, then seal the stain
Small dry stains can often be covered with a stain-blocking primer before painting; regular paint usually lets the stain bleed through. Damaged sections get cut out and replaced with new drywall, then taped, skim-coated and sanded so the repair disappears.
See it done
Here's a real water-damaged ceiling repair from start to finish, and a bathroom ceiling repair over a shower. Text a photo of your ceiling to (773) 886-5612.