How do I pronounce "Mädchen"?
An ä is not a sound that native English speakers make. It is not a short a like in “catch”. It is not a long a like in “made” either, though that is slightly closer. To me the closest vowel sound in English is a short e like in “end”.
The ch part is also not an English sound and it was harder for me to learn than ä. “ch” is sort of like how you would immitate a hissing cat. It is on the roof of your mouth in the back. That’s the best I can describe.
According to en.wiktionary.org:
IPA(key): /ˈmɛːtçən/ (used naturally in western Germany and Switzerland)
IPA(key): /ˈmeːtçən/ (overall more common; particularly northern and eastern regions)
So with the less common pronounciation of Mädchen in Germany, ɛː is the ä, wheras end has the same vowel ɛ (without the long suprasegmental symbol). The more common ponounciation uses a vowel not in English (eː)
According to wikipedia, æ (as in bad) is not used in standard German. https://en.wikipedia.org/wiki/Help:IPA/Standard_German