Touch the tip or front edge of your tongue to the roof of your mouth behind your teeth. Air flows through your nose.

Americans pronounce newton's as NOO-tuhnz (/ˈnuʔənz/). In "newton's", the "t" between vowels sounds like a quick "d" — the tongue briefly taps the ridge behind the upper teeth. This is called the Flap T, and it's why Americans sound more relaxed than the textbook. It comes out as NOO·tuhnz. Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "She explained Newton's laws of motion to the students".
Record yourself saying "newton's" 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.
Stop the air at your vocal cords (like the catch in 'uh-oh'). Your tongue doesn't need to touch the roof.

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.

Same position as S, but add vocal cord vibration. Feel the buzz.

The textbook way isn't wrong — it's just not how anyone actually says it.
In "newton's", the "t" between vowels sounds like a quick "d" — the tongue briefly taps the ridge behind the upper teeth. /t/ or /d/ becomes a quick tap [ɾ] — sounds like a soft D. The tongue briefly taps the ridge behind the upper teeth.
In "newton's", 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 NOO — 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.