Cleaning any type of jewellery can be tough, due to the delicate nature of the item. Gold watches for example, are precious to the majority of owners, so cleaning them properly is paramount.
We would recommend you start by cleaning the watch with a damp cloth. Rub the cloth gently over the gold plating, and hopefully in most cases that should be all you need to do. If your watch still has dirt, then we recommend trying to clean the dirty area with a bit of toothpaste. Rub over the area with a cleaning cloth. Once done use a soft toothbrush to clean the more tricky areas (grooves etc.) and you should notice the toothbrush have some grime appear. Make sure to use a wet cloth once done, to remove any toothpaste which may remain on the watch.