I went to the Canadian GP this year. Of course that venue is a lot different than Silverstone, but to some degree all F1 races are similar:
1) Becky's right - camping if the way to go, if you can do that. Find a friend with an RV or caravan or whatever you call it and invite him or her. If that fails, bring a tent. Drive to the track on Thursday evening. Park in a field as close as you can to your grandstand, then stake out your campsite. Put up a flag or something related to your favorite driver/team, break out the stereo and put on some good tunes, then break out the grill and the beer.
2) Bring a lot of beer. And some weed too, if you're into that. A lot of people in Montreal were smoking; we passed ours around quite a bit and everyone was grateful and very friendly.
3) Stuff at the track is expensive. Food was $6-10. A single 12oz beer can was $5.50. Avoid these prices by bringing a backpack full of beer and food with you to the track each day.
4) Bring some extra beer.
5) Make sure to bring earplugs and sunblock. Especially since 2006 with the switch to 2.4L V8s, F1 cars are extremely loud. It's literally staggering. At the beginning of first practice on Friday morning, I could only watch one of the Toro Rossos go by once before putting my earplugs in.
6) Make sure to bring enough beer.
7) I've never been to Silverstone (or anywhere in the UK, for that matter), but if I went I'd want to sit in the Stowe/Vale/Club area. The grandstand directly opposite the pits is usually hideously expensive and not worth the extra money. IMO, anyway.
8) Beer beer beer.