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

Americans pronounce coast as KOHST (/koʊst/). You'll hear it in sentences like "He's from a city near the coast" or "The old road goes over the cold ocean coast" — more examples below.
Record yourself saying "coast" 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.
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.
Place your tongue tip near the roof of your mouth behind your top teeth. Push air through the narrow gap. No voicing.

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 "coast", 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.