what do I do to stop my Apple Watch screen from moving up and down?

Hi

The behaviour that you have described is consistent with an issue with the Digital Crown's normal operation.

If your Apple Watch is worn too close to your hand, then the Digital Crown may be pressed by the back of your hand when flexing your wrist. If so:

• It may help to wear your Apple Watch a little further up your arm.
• It may otherwise help to wear your Apple Watch with the buttons on the other side and/or on your other wrist:

  To change the configuration: on your iPhone, in the Watch app, go to: My Watch (tab) > General > Watch Orientation > choose the preferred wrist and side for the buttons.

Otherwise, operation of the Digital Crown can be affected by substances like dust. Should it stop operating as expected, then it may help to clean it by following the steps here:

Use the Digital Crown on your Apple Watch - Apple Support

If the issue persists after following the recommended cleaning procedure, then I suggest that you contact Apple Support (remote diagnostics and/or mail-in service may be available, if required), make a Genius Bar reservation or visit an Apple Authorised Service Provider with a view to arranging for your watch to be checked and, if recommended, serviced:

• US: Apple Watch Service Answer Center - Apple Support
• Elsewhere: Apple - Support