Touch the front of your tongue to the roof of your mouth, then release into a 'sh' position. Flare your lips.

Americans pronounce cheap as CHEEP (/tʃip/). You'll hear it in sentences like "Which watch is cheap?" or "This cheap chip isn't very good" — more examples below.
Record yourself saying "cheap" 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.
Touch the front of your tongue to the roof of your mouth, then release into a 'sh' position. Flare your lips.

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

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 "cheap", 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.