Place your tongue tip near the roof of your mouth behind your top teeth. Push air through the narrow gap. No voicing.

Americans pronounce speedy as SPEE-dee (/ˈspidi/). In "speedy", the "t" between vowels sounds like a quick "d" — the tongue briefly taps the ridge behind the upper teeth. This is called the Flap T, a small move that separates 'classroom' from 'native'. So instead of SPEE·tee, you get SPEE·dee. Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "Everyone has the right to a fair and speedy trial".
Record yourself saying "speedy" and play it back. The mic stays on your device — nothing's uploaded.
2 syllables, 5 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Place your tongue tip near the roof of your mouth behind your top teeth. Push air through the narrow gap. No voicing.

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.

The textbook way isn't wrong — it's just not how anyone actually says it.
In "speedy", the "t" between vowels sounds like a quick "d" — the tongue briefly taps the ridge behind the upper teeth. /t/ or /d/ becomes a quick tap [ɾ] — sounds like a soft D. The tongue briefly taps the ridge behind the upper teeth.
Stress falls on the first syllable, not the others. Stretch SPEE — keep everything else short and quick.