Being a small town, the fastest and nicest way to get around is cycling, and indeed you will see a big lot of them everywhere, even to the point that the bike traffic is heavier than the car traffic here!
Don't worry if you don't own a bike here, you can always rent it directly at the train station, from Tommy Olsson at Lundahoj (there's the option of renting a tandem one if you're not alone :-)). Just check that it has a nice lock and that you never forget to lock it when you park it, since bike theft is the most common crime over here!
There's also a quite reliable bus network (stadbuss), and you can always check the timetables on line at the skanetrafiken site. The tickets cost 14SEK (€1.4) and are valid for one hour, this means you can make as many transfers between busses without having to pay again.
Cycling is a way of life in Lund. No other municipality in Sweden can match the frequency of bicycle travel achieved in Lund.