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

Americans pronounce persuasively as per-SWAY-suhv-lee (/pərˈsweɪsəvli/). Stress falls on the second syllable — keep everything else short and quick. You'll hear it in sentences like "She expressed her concerns eloquently and persuasively".
Record yourself saying "persuasively" and play it back. The mic stays on your device — nothing's uploaded.
4 syllables, 10 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.

Round your lips into a tight circle. Lift the back of your tongue toward the soft palate and add voice.

Start with your jaw slightly open and the front of your tongue forward and slightly up. Glide upward, your jaw closes a little more and your tongue arches higher toward the roof of the mouth.
Place your tongue tip near the roof of your mouth behind your top teeth. Push air through the narrow gap. No voicing.

Relax your lips, jaw, and tongue completely. Drop your jaw slightly and keep the tongue neutral.
Lift your bottom lip so its inner edge (where the wet part meets the dry part) touches the very bottom of your top front teeth. Add vocal cord vibration as you blow air through.

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.

The textbook way isn't wrong — it's just not how anyone actually says it.
Stress falls on the second syllable, not the others. Stretch SWAY — keep everything else short and quick.
Don't pronounce the second syllable too fully. The unstressed syllable reduces to a schwa — the lazy "uh" sound — in casual speech.
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.