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 vaccine as vak-SEEN (/vækˈsin/). Stress falls on the second syllable — keep everything else short and quick. You'll hear it in sentences like "The medical community is searching for a vaccine for the virus".
Record yourself saying "vaccine" and play it back. The mic stays on your device — nothing's uploaded.
2 syllables, 6 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 the jaw noticeably. Keep the body of the tongue low and forward, and don't let the back of the tongue raise toward the soft palate. Pull the lip corners back slightly, almost a starting smile.

Raise the back of your tongue to touch the soft palate (velum). Stop the air, then release.

Place your tongue tip near the roof of your mouth behind your top teeth. Push air through the narrow gap. No voicing.

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

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

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 SEEN — keep everything else short and quick.