Go to File at the menu bar to save your project. This is also where you can go to open your previous projects. When saving a project, it will only save as a GarageBand project. So when you click on the file you saved, it will reopen your project in GarageBand just how you last saved it.
Go to the menu bar Share > Export Song to Disk in order to export.
When exporting your project to a sound file you have multiple options. MP3/AAC is more compressed and therefore is a smaller file size.This is because it has less of the sound information on it, but it is standard enough so that it sounds close enough to the uncompressed file. WAVE/AIFF is less compressed and has more of the sound information on it and therefore is a bigger file size.
You have even more options at the export menu that pops up after choosing. This also allows you to save it to a location of your choosing.
When choosing MP3/AAC there are a couple other options.
When choosing WAVE/AIFF there are two options.
You also have the option to export just a selected region of your audio file by checking the box. You can do this using cycle (shown below). You can also export only selected regions by just selecting the audio clips you want to export.
