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

Americans pronounce covered as KUH-verd (/ˈkʌvərd/). Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "The moss covered the rocks near the stream" or "The mountain peak is covered in snow year-round" — more examples below.
Record yourself saying "covered" and play it back. The mic stays on your device — nothing's uploaded.
2 syllables, 5 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
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 "covered", 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 first syllable, not the others. Stretch KUH — keep everything else short and quick.
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.