In BrE, the front of the tongue rises to roughly the half-open position; the rims make slight contact with the upper molars. The lips are neutrally open.
I am not sure whether that helps much, I'm afraid. I have found that trying to create vowel sounds from a written description is not easy. In fact, I am following the above description as I write, and producing a variety of sounds in the region of /æ/; however, some of them approach /ʌ/, /ə/ or /ɜ/.
If I might venture a remark (I'm not a teacher, mind you, I only studied EFL): there are many on-line dictionaries offering audible (voice) pronunciation. Try listening to a number of words containing the /æ/ sound and see whether you can imitate the sound in a satisfactory manner.