When you're ready to test your kart, all you need to do is export it to the proper location and open up STK. In the Scene Properties section of Blender's properties window, find the Kart Exporter and hit Export. A file selector window will appear and you will need to go to the folder where your kart will be exported. This, of course, depends on your operating system. Make a folder for the kart under whichever of these paths is relevant:
- On Windows: %APPDATA%/supertuxkart/addons/karts
- On Linux: ~/.local/share/supertuxkart/addons/karts
- On macOS: ~/Library/Application Support/supertuxkart/addons/karts
then move to that directory in Blender and hit the SuperTuxKart Kart Export button. It may take several seconds to export the kart. When it has finished, copy any special texture files to the same directory as where you exported the kart. Then, open up STK and try out your new kart!