Press your lips together. Air flows through your nose. Vocal cords vibrate.

Americans pronounce monologue as MAH-nuh-lahg (/ˈmɑnəˌlɔɡ/). Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "The monologue was delivered with such emotion that people cried".
Record yourself saying "monologue" 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.
The schwa before L disappears — L becomes the vowel of the syllable. Go straight from the previous consonant to a Dark L.

Relax your lips and drop your jaw significantly. The tongue tip lightly touches behind the bottom front teeth and the back part of the tongue presses down a little to create more dark space in the back of the mouth.

Raise the back of your tongue to touch the soft palate. Add vocal cord vibration, then release.

The textbook way isn't wrong — it's just not how anyone actually says it.
In "monologue", the "g" 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 MAH — 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.