There's a pretty good chance you'll need some kind of antenna. In most cases, an indoor antenna will be fine for receiving digital broadcasts, but it really depends on where you live. If you live in a rural area (40-50 miles outside city limits), you may want to go with an outdoor antenna. I would suggest buying an indoor powered antenna first from a store with a good return policy.
Installation for an indoor antenna should be pretty quick, less than 5 minutes (One wire to connect to the converter), and the antenna itself is pretty easy to hide behind the TV due to its small size.
Once you get the antenna installed, turn on your TV, and do a scan for digital channels on your converter box. Once the scan is complete, you should be able to flip through the channels and receive a clear picture. If not, you may want to consider moving the location of the antenna, or upgrading to an outdoor antenna.