Drop your jaw slightly with relaxed lips. Touch the tongue tip behind the bottom front teeth and arch the top-front toward the roof.

Americans pronounce intermission as ihn-ter-MIH-shuhn (/ˌɪntərˈmɪʃən/). In "intermission", the "t" right after N is dropped — the tongue skips the T stop and moves directly from the N position to the next sound. This is called the Silent T after N, a hallmark of natural-sounding American speech. It comes out as IHN·ter·MIH·shuhn. Stress falls on the third syllable — keep everything else short and quick. You'll hear it in sentences like "The intermission gave us a chance to stretch our legs".
Record yourself saying "intermission" and play it back. The mic stays on your device — nothing's uploaded.
4 syllables, 9 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Flare your lips and lift the mid-front tongue close to the roof of your mouth. Blow air through without voicing.

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 "intermission", the "t" right after N is dropped — the tongue skips the T stop and moves directly from the N position to the next sound. /t/ is completely silent — the tongue skips the T stop and moves directly from the N position to the next sound.
In "intermission", 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 third syllable, not the others. Stretch MIH — keep everything else short and quick.
Don't pronounce the third syllable too fully. The unstressed syllable reduces to a schwa — the lazy "uh" sound — in casual speech.