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

Americans pronounce had as had (/hæd/). The "h" in "had" is dropped in connected speech — the preceding word's final consonant links directly to the remaining vowel — most natural in casual, rapid speech; in careful or formal speech, the H is typically kept. This is called the Silent H (in him, her, has), a quick, quiet beat that keeps content words in focus. It comes out as had. You'll hear it in sentences like "I had a strange dream last night" or "I had to guess some of the answers" — more examples below.
Record yourself saying "had" 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.

Drop the jaw noticeably. Keep the body of the tongue low and forward, and don't let the back of the tongue raise toward the soft palate. Pull the lip corners back slightly, almost a starting smile.

Touch the tip of your tongue to the roof of your mouth just behind your teeth. Add vocal cord vibration as you release.

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 "had", 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.