Memsource Editor is an application that is used for doing the actual translations. Anyone can install Memsource Editor for desktop use for free.
After you have installed the Editor, open a bilingual MXLIFF file in it to start translating. MXLIFF files can be downloaded from Memsource via the Download button under the Projects section.
The Memsource Editor will automatically connect you to the appropriate translation memory, term base, and/or machine translation in Memsource (do not forget to enter your login information by clicking on Tools and going to Preferences in the Editor).
Note: Make sure you have entered your login info in the Memsource Editor's Login Tab by going to Tools and selecting Preferences. Without logging in, you will not be able to connect to the translation memory, term base, and other centralized resources.