Most people arrive in Munich via the Munich International Airport (MUC) which is to the north west of the city center. It is connected to the city by S-Bahn (S8 and S1) which takes about 45 minutes and costs around €10. If you are in a group, you can buy a "Partner Card" which costs around €20 and is valid for all public transport in Munich for one day and up to 5 people.
Ryanair have started flying into Memmingen which they have dubbed "Munich West". The airport is indeed west of Munich, quite a long way west in fact - around 100km! That said, during the Oktoberfest it's not only Hotels in the city that are more expensive than usual - so are flights. Ryanair has very cheap deals to Memmingen, and there is a service to shuttle you to Munich for not too much more than the cost of a single S-Bahn ticket. It takes about twice as long though. There is also a shuttle bus to Memmingen train station, and from here you can take a train to Munich Hauptbahnhof.
Once you are in Munich, there are a number of public transport options available for getting to the Oktoberfest.
The most popular method is taking the U-Bahn (Subway) to Theresienwiese which is directly at the Oktoberfest grounds. The most popular route is not always the best though, especially during popular times where it can get a bit pushy.
If you do decide to take this station, one tip is to get on the first carriage if travelling west and the last carriage if travelling towards the east. This will ensure you end up right near the escalators to the grounds so you can get a head start and avoid most of the crush.
If you are going straight to the tents, it can be worth traveling a little further (or one stop shorter if coming from the west) on the U4/U5 line at Schwanthalerhöhe. In this case, you will want to be at the end of the train if traveling west, and the front carriage if traveling east . The back end of the tents are a short walk to the east after exiting the subway.
Another popular station is Hackerbrücke. It is a 5 minute or so walk away from the grounds (just follow the crowds) but is convenient because it is on the S-Bahn backbone that runs through the center of Munich.
Many visitors will arrive at Hauptbahnhof (Munich main station). It is actually possible to walk to the grounds from here in around 10 minutes, which is often easier and less confusing that changing trains.
Other options include Goetheplatz (south of the grounds, U3 and U6 lines) or Hermann-Lingg-Straße with Tram 18 or 19.
From any of the aforementioned stations, it is easy to find the grounds as there will be hundreds of other people going to there as well.
Driving to the Oktoberfest is, all in all, a very bad idea. There is no official parking at the grounds themselves, and all the street parking nearby will have long since been filled by Italians and their camper vans.