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

Americans pronounce cap as KAP (/kæp/). You'll hear it in sentences like "Did the cop leave his cap near the red cup" or "She forgot her swim cap and goggles at home" — more examples below.
Record yourself saying "cap" 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.

Drop the jaw noticeably. Keep the body of the tongue low and forward, and don't let the back of the tongue raise toward the soft palate. Pull the lip corners back slightly, almost a starting smile.

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

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 "cap", the "p" 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.