All the information in the past couple posts is pretty current. The main 3 areas people live are Shadyside, Oakland, or Squirrel Hill.
Shadyside is likely the most expensive, probably running at least $900 for a decent 1-bedroom. Regardless of area, having a person to split rent with will benefit you. Shadyside has a good amount to do, lots of restaurants, bars, shops, grocery stores, etc. The buses will take you to Pitt in about 10-15 minutes depending where in Shadyside you're coming from. Walnut Capital is a good leasing company, they're a bit more expensive, but they're really good about maintenance and helping with whatever you need.
Squirrel Hill is nice and quiet, but also has a main street (Murray Ave or Forbes Ave) that has pretty much whatever you need (grocery stores, restaurants, 2 or 3 somewhat ok bars, a few shops). It's a largely jewish neighborhood (40% is jewish) but the rest is made up with a lot of graduate students from both Carnegie Mellon and Pitt. Depending on where you are in Squirrel Hill you could be very close to Schenley Park, and once again there are many buses which will take you to Pitt in about 10-15 minutes.
Oakland is where Pitt is actually located, and is mostly where undergrads live. It's nice to be near the campus, but most grad students don't live there. It is cheaper, but you get what you pay for. I would probably advise against Oakland. Unless it's North Oakland on the edge of Shadyside.
Some people live out in bloomfield or friendship but you would definitely want a car as the buses come much less often and take much longer to get to campus, but I hear they are nice.
Hope this helps!