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

Americans pronounce gathered as GA-dherd (/ˈgæðərd/). Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "He gathered fallen leaves into a large pile" or "The dolphin gathered in a pod and swam near the boat" — more examples below.
Record yourself saying "gathered" 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.

Drop the jaw noticeably. Keep the body of the tongue low and forward, and don't let the back of the tongue raise toward the soft palate. Pull the lip corners back slightly, almost a starting smile.

Place your tongue tip between or behind your front teeth, turn your vocal cords on, and push air through the gap.
Relax your mouth and lift the tongue back and up. Keep the lips neutral.

Touch the tip of your tongue to the roof of your mouth just behind your teeth. Add vocal cord vibration as you release.

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.
In "gathered", the "d" 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 GA — 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.