If you open TableNinjaFT and an update is available there will be a pop-up at startup informing you of the update, and a link to download the update. If you click "remind me later" the program will launch normally and you can run the outdated version except there will be red text along the top letting you know an update is available.
To install the update just download the files and double click setup.exe. It will install on top of the existing installation and your, saved configurations, and log files will all remain untouched. Once the update is installed just run the program as normal.