October 17th, 2014: For information on what's new in 0.8.13, see the release announcement.
As noted in the release announcement you can can only update to this version incrementally from 0.8.12; for all other versions you will need to install it from scratch by installing one of the below .zip files.
To install Android Studio manually:
Windows: http://dl.google.com/dl/android/studio/ide-zips/0.8.13/android-studio-ide-135.1525417-windows.zip (169 MB)
Mac: http://dl.google.com/dl/android/studio/ide-zips/0.8.13/android-studio-ide-135.1525417-mac.zip (169 MB)
NOTE: These .zip files do not contain an embedded SDK install. If you have an existing install of Studio which contains an embedded SDK, if you upgrade by installing one of these zips, make sure you copy over the SDK as well.