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

Americans pronounce card as KARD (/kɑrd/). You'll hear it in sentences like "Send the card" or "Mark the card with a sharp marker" — more examples below.
Record yourself saying "card" 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.
Raise the back of your tongue to touch the soft palate (velum). Stop the air, then release.

Open wide for the 'ah' vowel. Lift the tongue back and up while flaring the lips for the 'r'.
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 "card", 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.
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.