Dress in business casual and arrive on time. Stay off of your phone. Smile. Speak if spoken to. Be friendly and courteous to the employees and patients. Don't address ANYONE by their first name unless invited to do so, particularly if the person is much older than you are or you are in the South.
Discretely make notes (or make mental notes) and google stuff you can learn from sources such as the websites from Mayo, Cleveland Clinic, Harvard, etc. (google elderly ankles, for example, to see reasons why an older adult may have swollen ankles). But you can also ask questions that show that you are curious and observant such as "what were you looking for when you examined the patient's ankles?" Don't try to show off by assuming a diagnosis ("based on those ankles, the patient has heart failure, right?")
If you see two patients with the same problem or the same diagnosis in a single shadowing session, you might ask, "do you have a large number of patients with X?" or "X seems pretty common. what proportion of your patients have X? Is it one of the most common reasons that patients see you?" follow up: "what are some of the other most common reasons for visits?" You might then read up on those common conditions so that you have more context the next time you shadow that doc. Best to ask questions when patients are not present. With any luck there will be time for a debrief during a shadowing visit.