Push a stream of air from your throat through your open mouth. No tongue or lip contact.

Americans pronounce hasn't as HA-zuhnt (/ˈhæzənt/). Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "The package hasn't arrived yet, has it?".
Record yourself saying "hasn't" and play it back. The mic stays on your device — nothing's uploaded.
2 syllables, 6 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Same position as S, but add vocal cord vibration. Feel the buzz.

Relax your lips, jaw, and tongue completely. Drop your jaw slightly and keep the tongue neutral.
The schwa before N disappears — N becomes the vowel of the syllable. Go straight from the previous consonant to N.

Touch the tip or front edge of your tongue to the roof of your mouth just behind your teeth. Keep your jaw relaxed. Stop the air, then release with a puff.

The textbook way isn't wrong — it's just not how anyone actually says it.
In "hasn't", the short unstressed vowel before "n" disappears — the schwa is absorbed and the "n" becomes the syllable nucleus on its own. Schwa is absorbed — consonant becomes the syllable nucleus.
Stress falls on the first syllable, not the others. Stretch HA — 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.