Both countries are part of the EU and signatories of the Schengen Treaty so the borders are open. You should still carry your passport with you, though.
Alternatively, you could also use the train. It's pretty fast and cheap going from Prague e.g. to Munich.
The Oktoberfest (or Wiesn as it's called by the locals) takes place in Munich, but contrary to its name, usually only about 3 days of it are in October, while two weeks are in September (this has historical reasons). This year it will be from 18th September to 4th October. There are plenty of rides and stands where you can buy different things (food, souvenirs) but it's basically about consuming large amounts of alcohol (like all German cultural events) with subsequent dancing on tables and benches. Also, the specially brewed beer for the occasion isn't actually very good. It comes in litre glasses and should be drunk while still cold. Choosing non-alcoholic beverages won't get you out of the dancing and singing along, though.
The breweries have their own tents and the atmosphere varies from tent to tent. It's not equally raucous everywhere. The tent preferred by younger people used to be "Schottenhammel" and the Hacker-Festzelt when I was there last (5 years ago). Since Augustiner is generally considered to be the best beer (make sure to sample it if you're in Munich and interested in beer) I suppose their Oktoberfest beer should be better, too. I've never been to their tent, though.
On weekends, it's very crowded.
