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

Americans pronounce points as POYNTS (/pɔɪnts/). In "points", 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, and it's one of the defining features of casual American English. It comes out as POYNTS. You'll hear it in sentences like "The team with the most points at the end wins" or "The judge deducted points for the shaky landing" — more examples below.
Record yourself saying "points" 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.
Press your lips together to stop the air, then release. No vocal cord vibration.

Start with rounded lips and tongue shifted back. Glide to relaxed lips with the tongue arching forward and up.
Touch the tip or front edge of your tongue to the roof of your mouth behind your teeth. Air flows through your nose.

The T is skipped entirely. Your tongue doesn't make contact at the T position.

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

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.
In "points", 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.