Press your lips together, add vocal cord vibration, then release.

Americans pronounce banana as buh-NA-nuh (/bəˈnænə/). In "banana", the "a" vowel before M or N raises and fronts toward [eə] — the tongue pulls up and forward, breaking the vowel into a tense glide as it anticipates the nasal. This is called the Cat-Vowel Before M/N, a hallmark of natural-sounding American speech. It comes out as buh·NA·nuh. Stress falls on the second syllable — keep everything else short and quick. You'll hear it in sentences like "A banana is a good source of potassium".
Record yourself saying "banana" and play it back. The mic stays on your device — nothing's uploaded.
3 syllables, 6 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Touch the tip or front edge of your tongue to the roof of your mouth behind your teeth. Air flows through your nose.

The tongue relaxes down in the back and the corners of the lips relax before the consonant. This adds a schwa-like 'uh' relaxation after the /æ/. Think of it as 'relaxing out of the vowel' — it is no longer a pure /æ/ sound.

The textbook way isn't wrong — it's just not how anyone actually says it.
In "banana", the "a" vowel before M or N raises and fronts toward [eə] — the tongue pulls up and forward, breaking the vowel into a tense glide as it anticipates the nasal. The "/æ/" vowel raises and fronts before M or N — tongue pulls up and forward, producing a tense [eə] glide (between /e/ and /ə/). Not a pure /æ/.
Stress falls on the second syllable, not the others. Stretch NA — keep everything else short and quick.
Don't pronounce the first syllable too fully. The unstressed syllable reduces to a schwa — the lazy "uh" sound — in casual speech.