Press your lips together, add vocal cord vibration, then release.

Americans pronounce born as BORN (/bɔrn/). You'll hear it in sentences like "Born in the morning" or "He was born in nineteen ninety-three" — more examples below.
Record yourself saying "born" 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.
Press your lips together, add vocal cord vibration, 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 behind your teeth. Air flows through your nose.

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.