QuickTabs allows you to save and open songs in 3 formats. You can save files using Ctrl+S or File->Save. If you are working on a song you opened, this will save it back to where you opened from. If you are working with a new never-been-saved song, it will open a file dialog. You may force the file dialog to open and save in a different location using Ctrl+Shift+S or File->Save as. You can open past saved files using Ctrl+O or File->Open.
QuickTabs JSON Format
Also known as .qtjson, this is the default save format. When in doubt, you pretty much cannot go wrong saving in this format. It is a direct representation of how QuickTabs remembers tab information serialized to json. Advantages of this format over others is it is very readable and editable from a text editor. Disadvantages include that is saves bigger files, but the files are still relatively tiny.
QuickTabs Bytecode Format
This is the bytecode and zlib compressed version of QuickTabs JSON Format. The extension for this format is .qtz. The only reason to save in this format over .qtjson is if you prefer very very tiny files. I have never been able to produce a .qtz that is larger than 1KB.
Midi Tab Format
This is an extension of Standard Midi File and is useful if you need to import the notes of your tab (other applications will not support the tab-specific data like tuning and which string to play on) into another application. You can also open from a non-modified midi tab file as it contains enough information to reconstruct the tab (not just a one way export.) You cannot use this format to attempt to open regular midi files saved by other applications, as normal midi files do not contain enough information to represent a tab.