Touch the front of your tongue to the roof of your mouth, then release into a 'zh' position. Add vocal cord vibration.

Americans pronounce jug as JUHG (/dʒʌg/). You'll hear it in sentences like "George enjoyed the large orange juice jug".
Record yourself saying "jug" 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.
Touch the front of your tongue to the roof of your mouth, then release into a 'zh' position. Add vocal cord vibration.

Relax your lips, jaw, and tongue completely. Drop your jaw slightly and keep the tongue neutral.
Raise the back of your tongue to touch the soft palate. Add vocal cord vibration, then release.

The textbook way isn't wrong — it's just not how anyone actually says it.
In "jug", the "g" 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.