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

Americans pronounce inspector as ihn-SPEHK-ter (/ɪnˈspɛktər/). Stress falls on the second syllable — keep everything else short and quick. You'll hear it in sentences like "The home inspector found issues that we needed to address immediately".
Record yourself saying "inspector" 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.
Place your tongue tip near the roof of your mouth behind your top teeth. Push air through the narrow gap. No voicing.

Press your lips together to stop the air, then release. No vocal cord vibration.

Drop your jaw moderately. Touch the tongue tip behind the bottom front teeth and lift the mid-front part slightly toward the roof.

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

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 "inspector", 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.
Stress falls on the second syllable, not the others. Stretch SPEHK — keep everything else short and quick.
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.