Cleaning depends on the case material, coating, water resistance and strap. The safest method is conservative: remove surface dust and oils without soaking or polishing unless the manufacturer allows it.
Check water resistance first
Do not immerse a watch simply because it once had a water-resistance rating. Gaskets age, crowns can be left open and vintage watches may no longer meet their original specification.
For coated or plated surfaces
Use a soft microfibre cloth with very light pressure. Abrasive polishes can remove or thin a decorative coating, so avoid them unless specifically approved for that finish.
Bracelet crevices
A very soft brush can help remove dry debris between links. If moisture is appropriate for your particular watch, use minimal amounts and dry the watch thoroughly.
When to use a professional
Valuable solid-gold, vintage or complicated watches are better handled by a watchmaker when deeper cleaning, polishing or case refinishing is required. Polishing permanently removes material and can change case geometry.