Flare your lips and lift the mid-front tongue close to the roof of your mouth. Blow air through without voicing.

Americans pronounce shot as SHAHT (/ʃɑt/). You'll hear it in sentences like "The buzzer beater shot won the game at the last second" or "I always get a flu shot before the winter season begins" — more examples below.
Record yourself saying "shot" 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.
Flare your lips and lift the mid-front tongue close to the roof of your mouth. Blow air through without voicing.

Relax your lips and drop your jaw significantly. The tongue tip lightly touches behind the bottom front teeth and the back part of the tongue presses down a little to create more dark space in the back 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 "shot", 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.