Touch the tip of your tongue to the roof of your mouth just behind your teeth. Add vocal cord vibration as you release.

Americans pronounce dimension as dih-MEHN-shuhn (/dɪˈmɛnʃən/). Stress falls on the second syllable — keep everything else short and quick.
Record yourself saying "dimension" and play it back. The mic stays on your device — nothing's uploaded.
3 syllables, 8 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Press your lips together. Air flows through your nose. Vocal cords vibrate.

Drop your jaw moderately. Touch the tongue tip behind the bottom front teeth and lift the mid-front part slightly toward the roof.

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

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.
Stress falls on the second syllable, not the others. Stretch MEHN — keep everything else short and quick.
Don't pronounce the second syllable too fully. The unstressed syllable reduces to a schwa — the lazy "uh" sound — in casual speech.