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

Americans pronounce gig as GIHG (/ɡɪɡ/). You'll hear it in sentences like "Begin the gig".
Record yourself saying "gig" 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.
Raise the back of your tongue to touch the soft palate. Add vocal cord vibration, then release.

Drop your jaw slightly with relaxed lips. Touch the tongue tip behind the bottom front teeth and arch the top-front toward the roof.

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 "gig", 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.