Go to oscars.org and register for tickets to sit in the bleachers that line the red carpet. Names will be drawn as part of a lottery system, as only 700 seats are available for members of the public. However, tickets are free, and it gives an incomparable view of celebrities as they arrive for the big event. While sitting in the bleachers won't get you inside the actual awards show, this is probably your best chance to attend the event.
Apply to be a "seat filler." Seat fillers literally fill the seats when celebrities and other attendees need to leave, so that when the camera pans across the audience, none of the seats look empty. You will spend the show getting up and down, and being seated in various locations, but you will at least be inside. Seatfiller.com accepts these applications.
Listen to local radio stations, read newspapers and watch local programming as the event draws closer. The Academy may release a limited number of tickets for giveaways. This very rarely happens, but it is possible.
Attend the event as a guest of someone with tickets. While most of us don't personally know famous celebrities, there's a possibility you may know someone who has worked on a nominated film, perhaps as a lighting technician or in wardrobe. Call your friends and see who knows who for your chance to attend.