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

Americans pronounce put as PUUT (/pʊt/). You'll hear it in sentences like "Put it on top" or "Put the pen down" — more examples below.
Record yourself saying "put" and play it back. The mic stays on your device — nothing's uploaded.
1 syllable, 3 sounds. 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.

Bring the corners of your lips in slightly so they push forward, but keep them relaxed. Lift the back of your tongue toward the roof of the mouth.

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.

Click any sentence to see the full breakdown — every link, every reduction, every flap-T.
The textbook way isn't wrong — it's just not how anyone actually says it.
In "put", 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.