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

Americans pronounce compete as kuhm-PEET (/kəmˈpit/). Stress falls on the second syllable — keep everything else short and quick. You'll hear it in sentences like "I learned to play chess and now compete in local tournaments".
Record yourself saying "compete" 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.
Press your lips together to stop the air, then release. No vocal cord vibration.

Pull the corners of your lips back slightly. Arch the middle-front of your tongue high toward the roof of the mouth.

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.

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 PEET — 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.