Raise the back of your tongue to touch the soft palate (velum). Stop the air, then release.

Americans pronounce county as KOWN-tee (/ˈkaʊnti/). In "county", 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, a hallmark of natural-sounding American speech. It comes out as KOWN·tee. Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "The sheriff is responsible for law enforcement in the county".
Record yourself saying "county" and play it back. The mic stays on your device — nothing's uploaded.
2 syllables, 5 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Raise the back of your tongue to touch the soft palate (velum). Stop the air, then release.

Start with a dropped jaw and flat tongue. Glide into a relaxed, slightly rounded lip position as the back of the tongue stretches 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 textbook way isn't wrong — it's just not how anyone actually says it.
In "county", 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.
Stress falls on the first syllable, not the others. Stretch KOWN — keep everything else short and quick.