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

Americans pronounce ferns as FURNZ (/fɜrnz/). You'll hear it in sentences like "The forest is dense with tall pine trees and ferns".
Record yourself saying "ferns" 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.
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.

Touch the tip or front edge of your tongue to the roof of your mouth behind your teeth. Air flows through your nose.

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

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.