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

Americans pronounce sheet as SHEET (/ʃit/). You'll hear it in sentences like "Can you fill this sheet out for me?" or "The choir director bought a quire of sheet music" — more examples below.
Record yourself saying "sheet" 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.

Pull the corners of your lips back slightly. Arch the middle-front of your tongue high toward the roof 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 "sheet", 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.