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

Americans pronounce groceries as GROH-suh-reez (/ˈgroʊsəriz/). Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "She clips coupons every week to save money on groceries".
Record yourself saying "groceries" and play it back. The mic stays on your device — nothing's uploaded.
3 syllables, 8 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 mouth slightly open, then close your jaw slightly as your lips round. Shift your tongue back slightly, then stretch the back up.
The schwa before R disappears — R becomes the vowel of the syllable. This is the 'er' sound without a distinct vowel before it.

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

Same position as S, but add vocal cord vibration. Feel the buzz.

The textbook way isn't wrong — it's just not how anyone actually says it.
Stress falls on the first syllable, not the others. Stretch GROH — 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.