Touch the tip or front edge of your tongue to the roof of your mouth just behind your teeth. Keep your jaw relaxed. Stop the air, then release with a puff.

Americans pronounce turnout as TURN-owt (/ˈtɜrnˌaʊt/). Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "Voter turnout was considerably higher than in previous elections".
Record yourself saying "turnout" and play it back. The mic stays on your device — nothing's uploaded.
2 syllables, 5 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Touch the tip or front edge of your tongue to the roof of your mouth just behind your teeth. Keep your jaw relaxed. Stop the air, then release with a puff.

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.

The textbook way isn't wrong — it's just not how anyone actually says it.
In "turnout", the "t" is not released — the articulators get into position but hold without the burst of air. Air stops but there's no release burst — the articulators hold position.
Stress falls on the first syllable, not the others. Stretch TURN — 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.