Maybe these web sites https://www.cs.tut.fi/~jkorpela/finnish.pronunciation.html and http://users.jyu.fi/~pamakine/kieli/suomi/aanneoppi/vokaaliten.html helps you to pronounce the letter ä.

Hi, Say "happy" and you say the letter ä. You say it "häppi" - Hamilton - Hämilton, hämillään - pan - pän, pätevä - pants - pänts, päivä - apple - äpple, älä - absolutely - äbsolutely, älyttömästi - dance - dänce, täällä Hope this helps :)

What my instructor recommended is to remember that it is a front vowel and should come from the front of your mouth. She said to think of smiling slightly when you say it to pull the sound forward. Good luck!