Drop your jaw moderately. Touch the tongue tip behind the bottom front teeth and lift the mid-front part slightly toward the roof.

Americans pronounce etymology as eh-tuh-MAH-luh-jee (/ˌɛɾəˈmɑlədʒi/). In "etymology", the "t" between vowels sounds like a quick "d" — the tongue briefly taps the ridge behind the upper teeth. This is called the Flap T, and it's why Americans sound more relaxed than the textbook. It comes out as EH·tuh·MAH·luh·jee. Stress falls on the third syllable — keep everything else short and quick. You'll hear it in sentences like "He is studying the etymology of words to better understand their meaning".
Record yourself saying "etymology" and play it back. The mic stays on your device — nothing's uploaded.
5 syllables, 9 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
The schwa before M disappears — M becomes the vowel of the syllable. Go straight from the previous consonant to M.

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.

Place the tip of your tongue against the alveolar ridge just behind your top front teeth, the same contact point as /t/, /d/, and /n/. The difference is what happens to the air: for /l/, you let it flow continuously around the <em>sides</em> of the tongue (that's why /l/ is called a lateral). Turn your voice on the whole time. Lips stay relaxed, no rounding or flaring. For the Dark L variant at the end of a syllable, also pull the back of the tongue up and back toward the soft palate.

Relax your lips, jaw, and tongue completely. Drop your jaw slightly and keep the tongue neutral.
Click any sentence to see the full breakdown — every link, every reduction, every flap-T.
The textbook way isn't wrong — it's just not how anyone actually says it.
In "etymology", the "t" between vowels sounds like a quick "d" — the tongue briefly taps the ridge behind the upper teeth. /t/ or /d/ becomes a quick tap [ɾ] — sounds like a soft D. The tongue briefly taps the ridge behind the upper teeth.
Stress falls on the third 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.