Place your tongue tip near the roof of your mouth behind your top teeth. Push air through the narrow gap. No voicing.

Americans pronounce square as SKWAIR (/skwɛr/). You'll hear it in sentences like "The fair hair was rare and square" or "Stare at the glare of the square flare" — more examples below.
Record yourself saying "square" 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.
Place your tongue tip near the roof of your mouth behind your top teeth. Push air through the narrow gap. No voicing.

Raise the back of your tongue to touch the soft palate (velum). Stop the air, then release.

Round your lips into a tight circle. Lift the back of your tongue toward the soft palate and add voice.

Start with the 'eh' vowel mouth position. Pull the tongue back and up while flaring the lips for the 'r'.
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.