Well, the first thing you should do is get a pair of skate shoes (check out the Best Skateboard Shoes List). You can skate in regular shoes, but it will be a lot harder and even sometimes dangerous. Skate shoes are built with a large flat bottom, to better grip the board, and often with other features like reinforcement in areas where you'll likely wear the shoe down.
You should also get a helmet (check out the Best Skateboard Helmets list). You might see skaters not wearing helmets, and worry that wearing one will make you look weak or stupid, but don't worry about it. It's common now for skateparks to require helmets, and it's just plain smart, especially when you first start out.
Wearing other protective pads can be good too, but what you need totally depends on what you are doing (see the Best Skateboard Pads list). If you are trying to do tricks in your driveway, elbow pads might be a good idea, but you really only need knee pads if you are skating on a ramp, or trying some pretty crazy tricks. Wrist braces can be nice, but be careful not to get too used to using your hands to catch yourself when you fall.