Raise the back of your tongue to touch the soft palate. Add vocal cord vibration, then release.

Americans pronounce greater as GRAY-ter (/ˈgreɪɾər/). In "greater", 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, and it's one of the defining features of casual American English. It comes out as GRAY·ter. Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "Advocates are calling for greater diversity in leadership positions".
Record yourself saying "greater" 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.
Raise the back of your tongue to touch the soft palate. Add vocal cord vibration, then release.

Curl or bunch your tongue without letting the tip touch the roof of your mouth. Brace the sides of your tongue against your upper back teeth, and round your lips slightly.
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.
The textbook way isn't wrong — it's just not how anyone actually says it.
In "greater", 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 GRAY — 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.