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 neurosurgeon as nuu-roh-SUR-juhn (/ˌnʊroʊˈsɜrdʒən/). Stress falls on the third syllable — keep everything else short and quick.
Record yourself saying "neurosurgeon" and play it back. The mic stays on your device — nothing's uploaded.
4 syllables, 9 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Curl or bunch your tongue without letting the tip touch the roof of your mouth. Brace the sides of your tongue against your upper back teeth, and round your lips slightly.
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 front of your tongue to the roof of your mouth, then release into a 'zh' position. Add vocal cord vibration.

Relax your lips, jaw, and tongue completely. Drop your jaw slightly and keep the tongue neutral.
The schwa before N disappears — N becomes the vowel of the syllable. Go straight from the previous consonant to N.

The textbook way isn't wrong — it's just not how anyone actually says it.
Stress falls on the third syllable, not the others. Stretch SUR — keep everything else short and quick.
Don't pronounce the third 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.