Pull the corners of your lips back slightly. Arch the middle-front of your tongue high toward the roof of the mouth.

Americans pronounce eaten as EE-tuhn (/ˈiʔən/). In "eaten", the "t" before the syllabic nasal becomes a glottal stop — a catch in the throat where the schwa drops and the nasal becomes syllabic. This is called the Glottal T, and it's why Americans sound more relaxed than the textbook. It comes out as EE·tuhn. Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "Have you eaten lunch yet?" or "I've eaten at that restaurant before" — more examples below.
Record yourself saying "eaten" and play it back. The mic stays on your device — nothing's uploaded.
2 syllables, 4 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.

The textbook way isn't wrong — it's just not how anyone actually says it.
In "eaten", the "t" before the syllabic nasal becomes a glottal stop — a catch in the throat where the schwa drops and the nasal becomes syllabic. /t/ becomes a glottal stop [ʔ] — a catch in the throat. The schwa in the following syllable is dropped, making the nasal syllabic.
In "eaten", 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 EE — 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.