Touch the tip or front edge of your tongue to the roof of your mouth behind your teeth. Air flows through your nose.

Americans pronounce noteworthy as NOHT-wur-dhee (/ˈnoʊtˌwɜrði/). Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "Your overall performance this year has been outstanding and noteworthy".
Record yourself saying "noteworthy" 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.
Touch the tip or front edge of your tongue to the roof of your mouth behind your teeth. Air flows through your nose.

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 just behind your teeth. Keep your jaw relaxed. Stop the air, then release with a puff.

The textbook way isn't wrong — it's just not how anyone actually says it.
In "noteworthy", 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 NOHT — 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.