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

Americans pronounce coat as KOHT (/koʊt/). You'll hear it in sentences like "Her threadbare coat was not warm enough" or "Please hang your coat in the living room" — more examples below.
Record yourself saying "coat" 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.
Raise the back of your tongue to touch the soft palate (velum). Stop the air, then release.

Start with your mouth slightly open, then close your jaw slightly as your lips round. Shift your tongue back slightly, then stretch the back up.
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 "coat", 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.