Place your tongue tip near the roof of your mouth behind your top teeth. Push air through the narrow gap. No voicing.

Americans pronounce smoothly as SMOODH-lee (/ˈsmuðli/). Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "I breathe smoothly" or "The relay team passed the baton smoothly without dropping it" — more examples below.
Record yourself saying "smoothly" and play it back. The mic stays on your device — nothing's uploaded.
2 syllables, 6 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Place your tongue tip near the roof of your mouth behind your top teeth. Push air through the narrow gap. No voicing.

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

Round your lips into a tight circle. Let your tongue rest in the middle of your mouth, slightly raised.
Place your tongue tip between or behind your front teeth, turn your vocal cords on, and push air through the gap.
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.

Pull the corners of your lips back slightly. Arch the middle-front of your tongue high toward the roof of the mouth.

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.
Stress falls on the first syllable, not the others. Stretch SMOODH — keep everything else short and quick.