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

Americans pronounce countertops as KOWN-ter-tahps (/ˈkaʊntərˌɾɑps/). In "countertops", 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 KOWN·ter·TAHPS. Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "I dusted all the shelves and wiped down the countertops".
Record yourself saying "countertops" and play it back. The mic stays on your device — nothing's uploaded.
3 syllables, 9 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.

Quickly bounce the front of your tongue against the roof of your mouth. Don't stop the airflow — just a quick tap.

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.

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

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 "countertops", 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.
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.