Touch the tip of your tongue to the roof of your mouth just behind your teeth. Add vocal cord vibration as you release.

Americans pronounce doctor's as DAHK-terz (/ˈdɑktərz/). Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "I have a doctor's appointment tomorrow morning" or "I have a doctor's appointment that I cannot reschedule unfortunately" — more examples below.
Record yourself saying "doctor's" and play it back. The mic stays on your device — nothing's uploaded.
2 syllables, 6 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Touch the tip of your tongue to the roof of your mouth just behind your teeth. Add vocal cord vibration as you release.

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.

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

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.

Relax your mouth and lift the tongue back and up. Keep the lips neutral.

Same position as S, but add vocal cord vibration. Feel the buzz.

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 "doctor's", 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 DAHK — 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.