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

Americans pronounce cried as krahyd (/kraɪd/). You'll hear it in sentences like "The monologue was delivered with such emotion that people cried".
Record yourself saying "cried" 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.

Curl or bunch your tongue without letting the tip touch the roof of your mouth. Brace the sides of your tongue against your upper back teeth, and round your lips slightly.
Start with your jaw open wide and your tongue resting low and flat. Glide the front of your tongue up toward the roof of your mouth as your jaw closes halfway.
Touch the tip of your tongue to the roof of your mouth just behind your teeth. Add vocal cord vibration as you release.

The textbook way isn't wrong — it's just not how anyone actually says it.
In "cried", the "d" 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.