Lift your bottom lip so its inner edge (where the wet part meets the dry part) touches the very bottom of your top front teeth. Add vocal cord vibration as you blow air through.

Americans pronounce vegetable as VEHJ-tuh-buhl (/ˈvɛdʒtəbəl/). The L in "vegetable" is a dark L — the back of the tongue rises toward the soft palate, adding a small "uh" quality before the L. This is called the Dark L vs Light L, and it's why Americans sound more relaxed than the textbook. It comes out as VEHJ·tuh·buhl. Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "He planted a vegetable garden in his backyard".
Record yourself saying "vegetable" 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.
Lift your bottom lip so its inner edge (where the wet part meets the dry part) touches the very bottom of your top front teeth. Add vocal cord vibration as you blow air through.

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 front of your tongue to the roof of your mouth, then release into a 'zh' position. Add vocal cord vibration.

The textbook way isn't wrong — it's just not how anyone actually says it.
The L in "vegetable" is a dark L — the back of the tongue rises toward the soft palate, adding a small "uh" quality before the L. Dark L adds a small schwa-like "uh" before the L. The back of the tongue lifts toward the soft palate.
Stress falls on the first syllable, not the others. Stretch VEHJ — 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.