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

Americans pronounce cornerstone as KOR-ner-stohn (/ˈkɔrnərˌstoʊn/). Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "The right to vote is a cornerstone of any democracy".
Record yourself saying "cornerstone" and play it back. The mic stays on your device — nothing's uploaded.
3 syllables, 8 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.

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.

Start with your mouth slightly open, then close your jaw slightly as your lips round. Shift your tongue back slightly, then stretch the back up.
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.
Stress falls on the first syllable, not the others. Stretch KOR — 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.