Touch the front of your tongue to the roof of your mouth, then release into a 'zh' position. Add vocal cord vibration.

Americans pronounce genome as JEE-nohm (/dʒinoʊm/). Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "The human genome project mapped all the genes in human DNA".
Record yourself saying "genome" 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 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.
Press your lips together. Air flows through your nose. Vocal cords vibrate.

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 JEE — keep everything else short and quick.