Swipe up from the bottom edge of your Apple Watch to get to the Control Center. There you will see a bell icon. When it is red with a strikethrough it is in mute mode. If you touch it, the button will go gray w/o the strikethrough which will then produce sounds when you get a notification.
Another thing to check is in your Apple Watch.app, make sure Notifications Indicator is on (green). Then make sure the apps listed show 'Mirror my iPhone' or 'Allow Notifications'.
Also look at Sounds & Haptics on Apple Watch.app on iPhone. Make sure Silent mode is not on, make sure the volume is up. Make sure Haptic Alerts are on (green).
If all else fails, then restart both your Apple Watch and your iPhone. Check again to see if all these are true and if it works. If it still does not omit sounds or vibrations. You're going to have to erase your Apple Watch by going to Settings, General, Reset. Then set it up again by pairing your watch again.
Todd
[Edited by Moderator]