Wikipedia has https://en.wikipedia.org/wiki/Help:IPA/Mandarin and https://en.wikipedia.org/wiki/Standard_Chinese_phonology Similar pages exist for many other languages. If you study the descriptions of the individual phones carefully, you should be able to consciously position your tongue and mouth to produce the correct sound.

E.g. the ü sound is https://en.wikipedia.org/wiki/Close_front_rounded_vowel , which means that it only differs from https://en.wikipedia.org/wiki/Close_front_unrounded_vowel (the English ee sound) by the lips being rounded instead of unrounded. English also has rounded vowels, for example https://en.wikipedia.org/wiki/Close_back_rounded_vowel (the oo sound). So you can learn to consciously pronounce ü by pronouncing ee and then rounding your lips as when pronouncing oo while keeping the tongue in the ee position.

Most teachers don't know enough about phonology to give that kind of explanation. My Mandarin teacher certainly didn't. I can only credit Wikipedia with helping me perfect my pronunciation to the point where I can be mistaken for a native speaker on the phone.