Living here is the fun part! For this transplant, anyway.
I'm pretty sure craigslist is used more than anything else. I've heard of people living everywhere from Long Island to the Upper West Side, but as far as Brooklyn neighborhoods go, Park Slope and Prospect Heights are probably the most popular. These dont come cheap but are very desirable places to live and work for most. Beware the mislabeling of neighborhoods by brokers - e.g. some dicey Crown Heights blocks will be marketed as Prospect Heights.
Some live in walking distance of the school in East Flatbush / PLG and do pretty well. The area around the Franklin stop in Crown Heights is gentrifying but still pretty affordable. If you dont mind a train transfer or using the bus, you can check out Sunset Park, Ditmas Park, Bed Stuy. One guy infamously rides his bike everyday from Red Hook.
There's a lot of other workable options, just look at a map and calculate your commute with hopstop or googlemaps. If money were no object I'd live in Greenwich Village.