>>939700815 (OP)
ö/ü in modern German derive from words where o/u collided with an i in Old High German, i.e. early medieval German. As a result, ö is between o and i, likewise ü is between u and i. Try pronouncing o and i and notice the movement that your mouth makes: o is with round lips and the tongue in the back, i has flat lips and the tongue in the front. Now pronounce o again and then slowly move the tongue forward, keeping the round lips. That's the "mouth position" for pronouncing ö. If you do it right, moving the tongue turns the o into an ö.
Similar for ü, the mouth position is very similar to when you're whistling (this is how i learned whistling as a kid, because i sometimes accidentally whistled when saying an ü).
If you can't get them right, DO NOT pronounce them as o and u, pronounce them as e and i, e.g. ich mechte instead of ich möchte. Many dialects do that, and many foreigners (especially slavs) that learned German, too...
