While in edit mode its the Arrow button on the upper left which provokes the Save dialog.
Exporting the project can only be done from within the gallery.
This is no help at all. The arrow does not invoke any save dialog! Please find me someone who actually knows the product.
Sent from my iPad
Just to clarify:
The 'back' arrow you see at the top left of the menu bar in PS touch only saves what you've been working on--or have modified (also as 'save as') as a .psdx file. This can of course be opened again in Touch, or exported via the Cloud (and by email) to your desktop if you want to work on it there.
From the main menu view, you can use the folder with an arrow, to upload to the cloud, save projects to the Gallery (as jpg ot png files), or share (in different file formats) via email, gmail, evernote, bluetooth, or send to other photo apps (these are the options on my tablet).