Welcome to the iPad version of Regina!
The best way to get to know Regina is simply to play around with it. Regina ships with several example files, which you can access through the Documents menu to your left.
For an excellent starting point, try Introductory examples.
To import your existing Regina or SnapPea/SnapPy documents, you can open them as email attachments, import them from Dropbox, or upload them through iTunes. To export a document from this app, press the share button in the top-right corner of the screen.
To create a new document, press the + button in the top-left corner of the screen.
The iPad version of Regina is very new, and offers most but not all of what Regina can do on the desktop. For more information on Regina, or to download a fully-featured desktop version, visit regina.sourceforge.net.
Enjoy!