Trains depart from København H (Copenhagen Central Station) every 20 minutes and the travel time is only 35 minutes to the centre of Malmö. You can also take a direct train to Malmö from Copenhagen Airport. You can get to Copenhagen Airport by both train and metro. Find train tickets here.
Please note that border authorities carry out ID inspection at Copenhagen Airport for travelers going to or from Malmö (or elsewhere in Sweden).
Tickets from the capital area to Southern Sweden are available for purchase at DSB Sales & Service within the capital area, 7-eleven stations or ticket machines.
Protip: Consider getting off at Triangelns Station which is one stop before Malmö Centralstation and boasts a quite spectacular arrival hall (pictured above). Above ground, you'll find the Triangeln shopping mall.