There is a bus from Lund a few times a day, and if you come from the near north, buses from Kristianstad (via several of the nice villages) is your best bet. Finally, you can also get here by bus from the ferries to Ystad. All this is easier on weekdays than weekends (with three or so buses on a Saturday) but still possible as long as you plan. The Ystad to Kristianstad bus is also doubling as the local bus between the villages around Simrishamn and thus, will also take you to Skillinge, Brantevik, Baskemölla and Kivik.
Getting around is perfectly OK by public transport Monday to Friday, but this unfortunately changes weekends when YOU are off :-) There are some local buses like between Ystad and Simrishamn along the coast, and Simrishamn to Kristianstad passing some nice villages, but having your own car is a lot easier, especially as some sights are in tiny villages with little public transport at the best of times. However, the best mode of transportation has to be the bike! The tourist offices in Simrishamn and Ystad can help you with lists of bike rental places (that is unless you put your own bike on the train from Malmö or Ystad harbour!) and also sell you packages with maps and B&B's. This way you can smell the apple orchards, hay meadows and the ever present sea. There are no major hills to conquer (although north of Simrishamn it gets hillier than south of it and there are always steep downhill runs to the seaside villages) and you have time to take in what Österlen is all about.
It is possible to get here without a car, just catch a train from Malmö or Ystad - you can even put your bike on the trains if it is not rush hour.