Push a stream of air from your throat through your open mouth. No tongue or lip contact.

Americans pronounce hate as HAYT (/heɪt/). You'll hear it in sentences like "Inhale the healthy air and exhale the hate".
Record yourself saying "hate" 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.
Push a stream of air from your throat through your open mouth. No tongue or lip contact.

Start with your jaw slightly open and the front of your tongue forward and slightly up. Glide upward, your jaw closes a little more and your tongue arches higher 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.

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