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

Americans pronounce salts as SAHLTS (/sɑlts/). In "salts", the "t" is squeezed between other consonants and drops out — the surrounding consonants flow together without it — most natural in flowing, casual speech; in careful or formal speech, the T may be lightly present. This is called the Silent T in Clusters, the kind of sound shift that makes everyday speech feel effortless. It comes out as SAHLTS. You'll hear it in sentences like "Acids and bases react to form salts and water".
Record yourself saying "salts" and play it back. The mic stays on your device — nothing's uploaded.
1 syllable, 5 sounds. 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.

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.

Keep the tongue tip down and pull the back of the tongue up toward the throat. The 'dark' sound comes from the back.

Touch the tip or front edge of your tongue to the roof of your mouth just behind your teeth. Keep your jaw relaxed. Stop the air, then release with a puff.

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

The textbook way isn't wrong — it's just not how anyone actually says it.
In "salts", the "t" is squeezed between other consonants and drops out — the surrounding consonants flow together without it — most natural in flowing, casual speech; in careful or formal speech, the T may be lightly present. /t/ is dropped entirely — the surrounding consonants flow together without the T.
The L in "salts" is a dark L — the back of the tongue rises toward the soft palate, adding a small "uh" quality before the L. Dark L adds a small schwa-like "uh" before the L. The back of the tongue lifts toward the soft palate.