Thinking aloud
Maybe the most important thing about shadowing sessions is that people think aloud. Basically they say:
What they are thinking out loud
What's the reasoning why they do things out loud
So that you, as the observer, not only see what's happening but also understand why it's happening.
How to make sure people think aloud
It's weird to think aloud, so here are a few tips that can help people do it:
Explain why it's important: explain why the fact that participants think aloud makes your job easier.
Explain what people should reveal out loud: explain that anything is relevant: doubts, reasoning, comments of how things feel, etc.
Make a demo: Show what people should say while doing a shadowing session by making an example where you are the participant.
Make a practice run: Use another exercise to make people get comfortable with the practice and for you to give feedback and encourage people on how to do so.
Remind people: Remind people to think aloud during the shadowing session