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 deepen as DEE-puhn (/ˈdipən/). Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "He taught the material to others to deepen his understanding".
Record yourself saying "deepen" and play it back. The mic stays on your device — nothing's uploaded.
2 syllables, 5 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 to stop the air, then release. No vocal cord vibration.

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 "deepen", 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 DEE — 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.