Relax your lips and drop your jaw significantly. The tongue tip lightly touches behind the bottom front teeth and the back part of the tongue presses down a little to create more dark space in the back of the mouth.

Americans pronounce odd as AHD (/ɑd/). You'll hear it in sentences like "Add the odd numbers" or "Add the odd code to the middle of the pad" — more examples below.
Record yourself saying "odd" and play it back. The mic stays on your device — nothing's uploaded.
1 syllable, 2 sounds. Explore each sound's mouth shape and how it's made.
Relax your lips and drop your jaw significantly. The tongue tip lightly touches behind the bottom front teeth and the back part of the tongue presses down a little to create more dark space in the back of the mouth.

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 "odd", 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.