Flare your lips and lift the mid-front tongue close to the roof of your mouth. Blow air through without voicing.

Americans pronounce sheer as SHEER (/ʃɪr/). You'll hear it in sentences like "Can you hear the sheer fear clearly?" or "A weird beard appeared on the sheer ear" — more examples below.
Record yourself saying "sheer" and play it back. The mic stays on your device — nothing's uploaded.
1 syllable, 2 sounds. Explore each sound's mouth shape and how it's made.
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.