I regularly do along to shoot my friend on track days. You can, indeed, wander around a lot of the track near the pits and the chicane. If you want to enter the pit lane you'll need a wristband.
Best places to shoot are:
The grassy bank near the toilet block - just across the track entry road from the pits. The cars will be accelerating away from the chicane, so not moving too fast (makes for easier panning). It's possible to find a location near the fence where you can get a clear view of the track.
The grassy bank on the outside of the track between the access road under the track and the Supershell huts. The section between Woodcote (the corner near Supershell) and the chicane is easy to access and you can get some good shots of cars cornering and then accelerating past.
I always shoot using manual exposure. I get a reading using spot metering on a bit of tarmac and use that to determine my shutter speed and aperture. I start with a fast shutter speed then as I get my eye in, slowly reduce it. By the end of a session I can get down quite low - this is 1/45s at 120mm using my 70-200f4