Press your lips together to stop the air, then release. No vocal cord vibration.

Americans pronounce prerequisite as pree-REH-kwuh-zuht (/ˌpriˈrɛkwəzət/). Stress falls on the second syllable — keep everything else short and quick. You'll hear it in sentences like "I need to complete the prerequisite course before advancing".
Record yourself saying "prerequisite" and play it back. The mic stays on your device — nothing's uploaded.
4 syllables, 11 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.

Curl or bunch your tongue without letting the tip touch the roof of your mouth. Brace the sides of your tongue against your upper back teeth, and round your lips slightly.
Pull the corners of your lips back slightly. Arch the middle-front of your tongue high toward the roof of the mouth.

Curl or bunch your tongue without letting the tip touch the roof of your mouth. Brace the sides of your tongue against your upper back teeth, and round your lips slightly.
Drop your jaw moderately. Touch the tongue tip behind the bottom front teeth and lift the mid-front part slightly toward the roof.

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

Round your lips into a tight circle. Lift the back of your tongue toward the soft palate and add voice.

Relax your lips, jaw, and tongue completely. Drop your jaw slightly and keep the tongue neutral.
Same position as S, but add vocal cord vibration. Feel the buzz.

Relax your lips, jaw, and tongue completely. Drop your jaw slightly and keep the tongue neutral.
Touch the tip or front edge of your tongue to the roof of your mouth just behind your teeth. Keep your jaw relaxed. Stop the air, then release with a puff.

The textbook way isn't wrong — it's just not how anyone actually says it.
In "prerequisite", the "t" is not released — the articulators get into position but hold without the burst of air. Air stops but there's no release burst — the articulators hold position.
Stress falls on the second syllable, not the others. Stretch REH — 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.