Place your tongue tip near the roof of your mouth behind your top teeth. Push air through the narrow gap. No voicing.

Americans pronounce stopwatch as STAHP-wahch (/ˈstɑpˌwɑtʃ/). Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "The stopwatch is used to time the sprints accurately".
Record yourself saying "stopwatch" and play it back. The mic stays on your device — nothing's uploaded.
2 syllables, 7 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.

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.

Relax your lips and drop your jaw significantly. The tongue tip lightly touches behind the bottom front teeth and the back part of the tongue presses down a little to create more dark space in the back of the mouth.

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

Round your lips into a tight circle. Lift the back of your tongue toward the soft palate and add voice.

Relax your lips and drop your jaw significantly. The tongue tip lightly touches behind the bottom front teeth and the back part of the tongue presses down a little to create more dark space in the back of the mouth.

Touch the front of your tongue to the roof of your mouth, then release into a 'sh' position. Flare your lips.

The textbook way isn't wrong — it's just not how anyone actually says it.
In "stopwatch", the "p" 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 first syllable, not the others. Stretch STAHP — keep everything else short and quick.