How do I change password when I forgot my old password

If by password, you are referring to the lock passcode for your Apple Watch, you may wish to just reset the watch. You can reset the watch which will erase all apps and data from it, then set it up again as new. Since most - if not all - watch apps use data from your iPhone, its very unlikely you will lose anything important other than time. Any cards you have added to wallet on the watch would need to be added again.

To reset the watch, open the Watch app on your iPhone, then select General > Reset > Erase Apple Watch Content and Settings