Lift your bottom lip to touch the very bottom of your top front teeth. Blow air through this contact point without voicing.

Americans pronounce firm as FURM (/fɜrm/). You'll hear it in sentences like "He disputed the call but the referee stood firm" or "The pasta should be cooked al dente, which means slightly firm" — more examples below.
Record yourself saying "firm" 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.
Lift your bottom lip to touch the very bottom of your top front teeth. Blow air through this contact point without voicing.

Flare your lips and push them away from the face. Lift the middle of your tongue toward the roof of the mouth.

Press your lips together. Air flows through your nose. Vocal cords vibrate.

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.