There are several types of transportation you can use to get from Copenhagen to Malmö and back; the distance between the cities isn't far. Your transportation options can usually be booked in advance, but each option has pros and cons:
1- Copenhagen to Malmö by Train
Taking the train from Copenhagen to Malmö is a very popular option and only takes 35 minutes across the famous Oresund Bridge. The train departs either city's central train station every 20 minutes, and stops intermittently (e.g. at Copenhagen Kastrup Airport). The advantage here is a flexible schedule and low price since you won't have to pay bridge toll. You can purchase your ticket locally, or order flexible train passes for Denmark and Sweden at RailEurope.com before you go so you don't have to worry about getting tickets.
2- Copenhagen to Malmö by Car
If you'd like to rent a car to get from Copenhagen to Malmö, it's a 45 minute drive (45 km / 28 mi). Simply take the E20 across the Oresund Bridge (toll required). A beautiful and memorable drive through the tunnel and across the bridge, but you'll pay for gas and the bridge toll.
3- Copenhagen to Malmö by BusFor around DKR 100, here's probably the cheapest option - take the Flybus 737 from Copenhagen to Malmo across the Oresund Bridge. It's a direct bus line commuting between the airports of the two cities, and also coincides with Ryanair flight arrivals from the UK. From Copenhagen, the bus to Malmö departs on Ingerslevsgade. In Malmö you'll find the bus to Copenhagen right outside Malmö airport. You can also take the greyhound bus (Gråhund), look for bus line 999.
You can also take a guided bus tour from Copenhagen to Malmö, such as the Swedish Day Trip from Copenhagen (unfortunately, it's not available year-round). This full-day tour contains bus and ferry transportation and guided group sightseeing of the Copenhagen-Malmö region.