When I try to charge my Apple Watch the apple logo comes on but it never charges. Is there something else I need to do?

First force restart it

i.e. press and hold both the side button and Digital Crown for at least 10 seconds, then release both buttons when you see the Apple logo.

If that is no help

 Unpair and erase your Apple Watch

On Youtube, https://www.youtube.com/watch?v=UXBcNcbTcqg&list=RDCMUCYFQ33UIPERYx8-ZHucZbDA&start_radio=1&rv=UXBcNcbTcqg&t=25

and then

Set up your Apple Watch

Or in Youtube https://www.youtube.com/watch?v=7rb3vX86RUQ&list=RDCMUCYFQ33UIPERYx8-ZHucZbDA&index=3

 If no better you may want to unpair then set up without restoring the backup.

If still no good ensure you have no security apps on the iphone that may be mirrored on the Watch.

You may also want to make sure the software on the watch is up to date.

Update your Apple Watch

If you've completed that troubleshooting or you can't get past the forced restart and the issue is still not resolved, Contact Support.

Click here > Contact - Official Apple Support

or phone numbers 

Click here > Contact Apple for support and service - Apple Support