How can I pronounce 绿 (lü4 - green)?
The sound represented by the ü sound in Chinese is the same as the German ü; this sound is a close front rounded vowel, the IPA is [y]; you can hear a sample in the link.

As you see in the table below in that wikipedia article, which lists the languages that possess this sound, we see both Mandarin (which uses green as the example) and German. So the sound is the same.

The best way to teach this is:


Pronounce an "ee" sound, in English, like for "feel".
Keep pronouncing the sound, but start rounding your lips as if you had to pronounce a "oo" sound, which is [u], a close back rounded vowel.
The final sound you should get is the one of a close front rounded vowel, also written as [y].


Basically, you have the same lips position for U and Ü, but a different tongue position, the one for the [i] sound.

Look at the image below. The tongue position is different in [i] (upper-left) and [u] (upper-right).

 (Source)