Drop your jaw slightly with relaxed lips. Touch the tongue tip behind the bottom front teeth and arch the top-front toward the roof.

Americans pronounce internet as IHN-ter-neht (/ˈɪntərˌnɛt/). In "internet", the "t" right after N is dropped — the tongue skips the T stop and moves directly from the N position to the next sound. This is called the Silent T after N, and it's why Americans sound more relaxed than the textbook. It comes out as IHN·ter·NEHT. Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "My computer isn't connecting to the internet" or "The internet of things connects billions of devices worldwide" — more examples below.
Record yourself saying "internet" and play it back. The mic stays on your device — nothing's uploaded.
3 syllables, 7 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Touch the tip or front edge of your tongue to the roof of your mouth behind your teeth. Air flows through your nose.

Drop your jaw moderately. Touch the tongue tip behind the bottom front teeth and lift the mid-front part slightly toward the roof.

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.

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 "internet", the "t" right after N is dropped — the tongue skips the T stop and moves directly from the N position to the next sound. /t/ is completely silent — the tongue skips the T stop and moves directly from the N position to the next sound.
In "internet", the "t" is not released — the articulators get into position but hold without the burst of air. Air stops but there's no release burst — the articulators hold position.
Stress falls on the first syllable, not the others. Stretch IHN — 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.