Flare your lips and lift the mid-front tongue close to the roof of your mouth. Blow air through without voicing.

Americans pronounce short as SHORT (/ʃɔrt/). You'll hear it in sentences like "She wore a short dress" or "The short sport report was sort of poor" — more examples below.
Record yourself saying "short" and play it back. The mic stays on your device — nothing's uploaded.
1 syllable, 3 sounds. Explore each sound's mouth shape and how it's made.
Flare your lips and lift the mid-front tongue close to the roof of your mouth. Blow air through without voicing.

Start with the 'aw' jaw drop and rounded lips. Pull the tongue back and up while keeping the lips rounded for the R.
Touch the tip or front edge of your tongue to the roof of your mouth just behind your teeth. Keep your jaw relaxed. Stop the air, then release with a puff.

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 "short", the "t" 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.
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.