You can check for software updates from the Settings -> About tab. An internet connection is required for this.
By default the application will check for updates upon starting. This behavior can be changed by unchecking the 'Automatically check for new updates' setting on this tab.
If a new update is available a dialog box will appear which will give you the option of visiting the Duplicate Cleaner download page to download the new version. The update can simply be installed over your current version - all settings and registration details will be retained, though you will need to close the program before installing.