By bus
Gråhundbus (http://www.graahundbus.dk...), Swebus (http://www.swebus.se/), GoByBus (http://www.gobybus.se/) and Eurolines (http://www.eurolines-trav...) have routes to Copenhagen and other places. To Copenhagen the buses take longer about an hour but are cheaper than the train, especially for day trips.
By plane
Both Malmö Airport Sturup (http://www.lfv.se/sv/Malm...) and Copenhagen Airport Kastrup (http://www.cph.dk/CPH/UK/MAIN/) serve Malmö. If you get to the Malmö Airport you'll then have to take the bus shuttle service to downtown Malmö, but first check the schedules at Flygbussarna's homepage (http://www.flygbussarna.s...) because on Saturday afternoons they don't have many buses. From Copenhagen Airport you can either take the train or the bus, bus being the cheapest option.
By train
Malmö has 7 train stations: Malmö Centralstation, Triangeln, Hyllie, Persborg, Svågertorp, Oxie, and Burlöv.
Trains from Copenhagen take 25 minutes from København H Copenhagen Central Station to Malmö. They leave all day from Elsinore Helsingør, traversing the east coast of Sjælland, before crossing through Copenhagen and then across the Ãresund bridge to Malmö, also connecting Kastrup airport to the city. Since the December 2010 opening of the Citytunneln, trains now travel every 10 minutes directly to Malmö Central, with a stop at the new Triangeln station in the city center. Expect to pay 190 SEK for a return ticket to Kastrup airport or Copenhagen Central.
There are about ten daily X2000 trains (http://www.sj.se/sj/jsp/p...) to Stockholm and roughly 100 daily departures for the nearby university town of Lund 17 km north. For travel northward, there are hourly services to Helsingborg and Gothenburg with connections to Oslo. There is also a overnight service connecting Malmö to Berlin (http://www.berlin-night-e...) running nightly or every second night depending on season.
Night trains depart for Storlien Friday and Sunday with connection to Trondheim. For every-night connection, grab a train or bus for Gothenburg.
Frequent and regular local trains go from Malmö south throughout the province of Scania to Lund, Helsingborg, Höör and Ystad. These are known as Pågatågen, operated by Skåne Commuter Rail.
By car
If you don't take the train across the bridge and tunnel, you can drive for yourself. It is a pay bridge, where you pay to enter Sweden 250 DKK in 2008 (http://uk.oresundsbron.co...), after you go through the tunnel and across the bridge, and then it costs the same to come back. The view is much less obstructed if you choose to go by car as compared to train. (http://www.oeresundsbron.com)