The steel case
The first thing to do before cleaning your case is to dismantle the bracelet if it is not waterproof. Also check that the crown is perfectly locked otherwise the water could enter the housing.
If your case is waterproof (at least 50m or 5 ATM), you can clean with a soft brush soaked in soapy water (an old toothbrush will be ideal!). Soap or shampoo are perfect. Rub gently and rinse under clear water. Then dry well with a soft, dry cloth.
Model not waterproof
If your housing is not waterproof, you do not need direct contact with the water. In this case, use a microfiber cloth or a chamois leather (glasses cloth). Lightly moisten the fabric (it must be thoroughly wrung out) and rub gently to clean. For nooks, a soft toothbrush or a cotton swab will better dislodge dirt that the rag can not reach.
Once the surface is clean, dry with a dry cloth this time.
For the glass, it is possible to clean with a soft cloth soaked in Miror (cleaning product) by rubbing in small circles.
Steel / rubber bracelet
As with the waterproof case, use a soft brush with soap then rinse before completely drying the strap with a dry cloth.
There are also commercially available ultrasonic machines whose vibrations under water can remove dirt. If you use one of these machines, take care to remove the case before plunging the bracelet into the water.
To clean it, wipe a soft, damp brush with a little soap and scrub gently (inside and outside), emphasizing the seams. Then rinse with clean water (soaked brush, no direct contact with water) and let dry naturally. Be careful not to put it on a radiator or near any other source of heat.
Good to know
If you want to clean the inside of the watch, ie the movement, it is imperative to call on a jeweler or a watch manufacturer.
For a better life of your watch, you must have it checked every 3 to 4 years, especially if it is waterproof to check the condition of the joints.
Even if your timepiece is waterproof, always consider rinsing it after swimming in the sea or in a swimming pool. The ideal is obviously not to wear during this kind of activities.
Beware of the tasks that can cause cosmetics, perfumes or chemicals.