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

Americans pronounce cards as KARDZ (/kɑrdz/). You'll hear it in sentences like "Do you accept credit cards here?" or "Pick the pack of cards from the back pocket" — more examples below.
Record yourself saying "cards" and play it back. The mic stays on your device — nothing's uploaded.
1 syllable, 4 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.

Same position as S, but add vocal cord vibration. Feel the buzz.

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.
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.