Press your lips together to stop the air, then release. No vocal cord vibration.

Americans pronounce purely as PYUUR-lee (/ˈpjʊrli/). Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "The fury of the jury was purely mature" or "I prefer visual learning materials over purely text-based resources" — more examples below.
Record yourself saying "purely" 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.
Press your lips together to stop the air, then release. No vocal cord vibration.

Lift the middle of your tongue toward the roof of your mouth, but stop just short of touching. /j/ is an approximant, not a stop. The tongue tip stays down, lightly resting near the back of your bottom front teeth. Voice runs through the whole gesture, and the tongue glides smoothly down into the next vowel. The lips stay neutral or pre-shape for the upcoming vowel (rounding early for OO in <em>youth</em>, for example).

Start with the 'uu' position. Pull the tongue back and up while maintaining the lip flare.
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 PYUUR — keep everything else short and quick.
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.