We were staying in Denmark so we took the long bridge across the channel. It was cool because I believe it is either the longest or second longest bridge in the world. However, it wasn't cheap. It cost us almost $50 to cross over to Sweden and back to Denmark.
I parked at a large parking lot across the main train station. There will be plenty of signs directing you to the train station. When we crossed the bridge from Denmark there was a tourist information center shortly after getting off the bridge and onto the land. They gave us a map of Malmö which was very helpful, the staff there were very pleasant and helpful to all the tourists.
If you come from Copenhagen you can come by train or by boat. Both options are equally good. I went there by train (I wanted to experience the crossing of the Øresund bridge) and came back by boat. I preferred the boat, but I must say the sea was very calm that day.
Malmö is not very big and you can walk everywhere. If you want to go to the beach (not a great view except in summer), you can rent a bike.
Surprisingly enough, the best way to get to Malmo (Sweden) is from... Copenhagen (that's what I did myself). Well, not that surprising, maybe, when you consider that it takes a train much less than an hour to get from the Central Station and Airport of Copenhagen to Malmo. There are also good railway and road connections with other places in Scandinavia.
I went around on foot, and that was OK with me...