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

Americans pronounce courts as KORTS (/kɔrts/). You'll hear it in sentences like "The maritime dispute has been referred to international courts".
Record yourself saying "courts" 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.

Start with the 'aw' jaw drop and rounded lips. Pull the tongue back and up while keeping the lips rounded for the R.
Touch the tip or front edge of your tongue to the roof of your mouth just behind your teeth. Keep your jaw relaxed. Stop the air, then release with a puff.

Place your tongue tip near the roof of your mouth behind your top teeth. Push air through the narrow gap. No voicing.

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.