Follow the instructions here, including contacting Apple Support (mail-in service may be available, if required), making a Genius Bar reservation or visiting an Apple Authorised Service Provider if necessary:
- Check your battery and charge your Apple Watch - Apple Support
- If your Apple Watch won't charge or it won't turn on - Apple Support
If your Apple Watch is turned off before being placed on the charger, connected to power, then note that it can take a few minutes for it to turn on (which happens automatically). It is also normal for the display to sleep after charging has started. To check on progress, tap on the screen.