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.

Americans pronounce teammate as TEEM-mayt (/ˈtimˌmeɪt/). Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "She passed the ball to her teammate who was open".
Record yourself saying "teammate" 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 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.

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

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

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

Start with your jaw slightly open and the front of your tongue forward and slightly up. Glide upward, your jaw closes a little more and your tongue arches higher 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.
In "teammate", 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 TEEM — keep everything else short and quick.