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

Americans pronounce fury as FYUUR-ee (/ˈfjʊri/). Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "The fury of the jury was purely mature".
Record yourself saying "fury" and play it back. The mic stays on your device — nothing's uploaded.
2 syllables, 4 sounds. Tap a syllable to jump to its row, then 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.

Lift the middle of your tongue toward the roof of your mouth, but stop just short of touching. /j/ is an approximant, not a stop. The tongue tip stays down, lightly resting near the back of your bottom front teeth. Voice runs through the whole gesture, and the tongue glides smoothly down into the next vowel. The lips stay neutral or pre-shape for the upcoming vowel (rounding early for OO in <em>youth</em>, for example).

Start with the 'uu' position. Pull the tongue back and up while maintaining the lip flare.
The textbook way isn't wrong — it's just not how anyone actually says it.
Stress falls on the first syllable, not the others. Stretch FYUUR — keep everything else short and quick.
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.