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

Americans pronounce discovered as duh-SKUH-verd (/dəˈskʌvərd/). Stress falls on the second syllable — keep everything else short and quick. You'll hear it in sentences like "He explored the caves and discovered ancient rock art" or "I discovered that I am an auditory learner through experience" — more examples below.
Record yourself saying "discovered" and play it back. The mic stays on your device — nothing's uploaded.
3 syllables, 8 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Place your tongue tip near the roof of your mouth behind your top teeth. Push air through the narrow gap. No voicing.

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

Relax your lips, jaw, and tongue completely. Drop your jaw slightly and keep the tongue neutral.
Lift your bottom lip so its inner edge (where the wet part meets the dry part) touches the very bottom of your top front teeth. Add vocal cord vibration as you blow air through.

Relax your mouth and lift the tongue back and up. Keep the lips neutral.

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 "discovered", 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.
Stress falls on the second syllable, not the others. Stretch SKUH — keep everything else short and quick.
Don't pronounce the first syllable too fully. The unstressed syllable reduces to a schwa — the lazy "uh" sound — in casual speech.
Americans use a relaxed retroflex R — the tongue curls back rather than rolling. The R is one continuous sound with the vowel before it, not two separate sounds.