Raise the back of your tongue to touch the soft palate (velum). Stop the air, then release.

Americans pronounce careers as kuh-REERZ (/kəˈrɪrz/). Stress falls on the second syllable — keep everything else short and quick. You'll hear it in sentences like "Why did you decide to change careers?".
Record yourself saying "careers" 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.
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 the high 'ih' position. Pull the tongue back and up while flaring the lips slightly.
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 second syllable, not the others. Stretch REERZ — 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.
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.