Excuse the mess
You will see a lot of occupied rooms; try to look beyond the mess. Sometimes the current tenant will be in the apartment. Be respectful and direct your questions to the agent.
Depending on the building and timing of the viewing, you might be shown a comparable unit; this is the exact same unit on a lower or higher floor. The floor plan and view will be the same unless it's on a much higher or lower floor. This is fine for the viewing, but before you sign a lease, make sure you see the actual unit. The conditions and appliances may differ, or it might be next to a loud laundry room or a super's closet, etc.
How long can I spend?
Try not to stay longer than twenty minutes, especially if the tenant is there. But do take the time you need and ask questions; remember, it might be gone soon.
Can I take pictures?
Not if it's occupied. For empty units, it's usually okay. In luxury buildings, sometimes staff won't want pictures taken. A good rule of thumb: always ask first.