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

Americans pronounce point as POYNT (/pɔɪnt/). You'll hear it in sentences like "Point to the coin" or "Join the coin joint for a joyful point" — more examples below.
Record yourself saying "point" and play it back. The mic stays on your device — nothing's uploaded.
1 syllable, 4 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.

Start with rounded lips and tongue shifted back. Glide to relaxed lips with the tongue arching forward and up.
Touch the tip or front edge of your tongue to the roof of your mouth behind your teeth. Air flows through your nose.

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 "point", 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.