Touch the tip of your tongue to the roof of your mouth just behind your teeth. Add vocal cord vibration as you release.

Americans pronounce dinosaurs as DAHY-nuh-sorz (/ˈdaɪnəˌsɔrz/). Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "She is interested in paleontology and the study of dinosaurs".
Record yourself saying "dinosaurs" and play it back. The mic stays on your device — nothing's uploaded.
3 syllables, 7 sounds. Tap a syllable to jump to its row, then 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.

Start with the 'aw' jaw drop and rounded lips. Pull the tongue back and up while keeping the lips rounded for the R.
Same position as S, but add vocal cord vibration. Feel the buzz.

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 DAHY — keep everything else short and quick.
Don't pronounce the first syllable too fully. The unstressed syllable reduces to a schwa — the lazy "uh" sound — in casual speech.
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.