How did you buy Aperture? Is it an AppStore version or a pre-AppStore version with a registration number?
For the pre-AppStore version use Software update from the Apple menu; for an AppStore version look at the "Updates" tab of the AppStore.
You need to be signed into the AppStore with you AppleID when you are doing this.
Also Aperture needs to be installed in your Applications folder, not in a subfolder of Applications, and simple be called Aperture, without any added version numbers.
For some persons the update only worked, after setting the primary system language to English U.S. in the Languge & Text System Preferences and rebooting before trying to update.