TortoiseGit is like any other application and should be updated when an update is available. Fortunately, it comes with automatic updates includes. You will receive a popup telling you there is an update available; click Download to download the new version:
When I started developing plugins for ClassicPress I decided that I needed to be using source control. As ClassicPress is intending to use GitHub for their plugin directory, it made sense for me to use it as well. This post is part of a series on ClassicPress Development with TortoiseGit which is a sub-series of the ClassicPress Development with GitHub series.