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

Americans pronounce slang as SLANG (/slæŋ/). In "slang", the "a" vowel before NG shifts toward "ay" — sounding like "ay" as in "say", a distinctly American pattern — most prominent in Midwestern American English; other GenAm speakers may use a less raised vowel. This is called the Cat-Vowel Before NG, and it's why Americans sound more relaxed than the textbook. It comes out as SLANG. You'll hear it in sentences like "I learned a lot of slang and idioms from watching television shows".
Record yourself saying "slang" and play it back. The mic stays on your device — nothing's uploaded.
1 syllable, 4 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.

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.

Before NG, the vowel changes to sound more like the AY (/eɪ/) diphthong. The middle part of the tongue lifts toward the roof of the mouth, then the front part arches up.

Lift the back of your tongue to the soft palate. Lower your soft palate to let air flow through your nose.

The textbook way isn't wrong — it's just not how anyone actually says it.
In "slang", the "a" vowel before NG shifts toward "ay" — sounding like "ay" as in "say", a distinctly American pattern — most prominent in Midwestern American English; other GenAm speakers may use a less raised vowel. Vowel changes to sound like /eɪ/ ("ay" as in "say").