Start by turning the radiator off and letting it go stone cold. Painting a warm radiator is the fastest route to a streaky, blistered mess — the paint flashes off before you've laid it flat.
Clean it properly first. Sugar soap to shift dust, grease and any old polish, then rinse and let it dry. Give the whole thing a light sanding with 240-grit to key the surface — paint needs something to grab onto, especially on that glossy factory finish. Mask the wall behind and the valves with FrogTape.
If there's any bare or rusty metal showing, spot-prime it. Zinsser Cover Stain or a metal primer sorts rust and stops it bleeding through. On a sound, previously painted radiator in good nick you can usually go straight over with a quick key and skip the full prime.
For the topcoat, you've got two routes. The traditional one is a dedicated radiator enamel — heat-resistant and tough. But honestly, most decent water-based satinwood and eggshell trim paints now handle radiator heat fine and won't yellow, which is the big advantage. Little Greene Intelligent Eggshell and Dulux trim formulas both cope happily. The old problem of white radiators going custard-yellow was an oil-based, non-drying-oil issue — modern acrylics don't do it.
Apply two thin coats, not one thick one. Use a 50mm radiator brush or a long-pile mini roller to reach behind, and lay off in the direction of the metal. Thin coats dry harder and avoid runs in the recesses.
Colour-wise, most people want it to disappear into the wall. Match it to your trim or wall colour — Farrow & Ball Pointing or Slipper Satin for a soft off-white, or go bold and paint it the wall colour like Mole's Breath so it reads as one surface.
Leave it a good few days before firing the heating back up. Curing under heat too early traps solvent and softens the finish — patience here pays off.