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

Americans pronounce beer as BEER (/bɪr/). It's 2 sounds in 1 syllable. The R curls back and blends into the vowel — they sound as one continuous unit.
Record yourself saying "beer" 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.