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

Americans pronounce contemporary as kuhn-TEHM-puh-reh-ree (/kənˈtɛmpəˌrɛri/). Stress falls on the second syllable — keep everything else short and quick. You'll hear it in sentences like "The seminar focused on contemporary issues in environmental science".
Record yourself saying "contemporary" and play it back. The mic stays on your device — nothing's uploaded.
5 syllables, 12 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.

Relax your lips, jaw, and tongue completely. Drop your jaw slightly and keep the tongue neutral.
Touch the tip or front edge of your tongue to the roof of your mouth behind your teeth. Air flows through your nose.

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.

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

Press your lips together. Air flows through your nose. Vocal cords vibrate.

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.
Stress falls on the second syllable, not the others. Stretch TEHM — keep everything else short and quick.
Don't pronounce the first syllable too fully. The unstressed syllable reduces to a schwa — the lazy "uh" sound — in casual speech.