Brown water stain on the ceiling — how do I fix and repaint it?

Can confirm — I repainted without stain-block first and the brown came back within a week. Primer sorted it.

One to add once you've fixed the leak and stain-blocked it: the finish you repaint in matters as much as the colour, especially in a bathroom or kitchen where damp and wiping are a factor. There's a thread on which paint finish — matt, eggshell, satin or gloss — belongs in which room. Stain-blocking primer first, then the right sheen on top, so the repaint not only hides the mark but actually stands up to how the room gets used.

One prevention point that ties into ceiling stains: in a damp room (bathroom, kitchen, utility), the board itself matters. Standard plasterboard soaks up humidity and is far more prone to sagging, staining and mould than moisture-resistant (green) board, which resists it. So while a brown stain is usually a leak to trace and fix (as above), boarding a damp room in the right material stops the everyday humidity version. There's a thread on where to use moisture-resistant (green) gypsum board — and why it isn't waterproof. Fix the leak here; but if a ceiling's in a wet room, spec MR board when it's redone.