Keynote app for iOS can open, edit and save presentations and can import presentations created on your Mac as well as share your presentations back to your Mac.
The most common way to share files is via iTunes but files can also be shared via email (with some size limitations), Dropbox and other similar apps. Keynote on an iOS device can save and share files to iCloud with other iOS devices, but Keynote for OSX can't directly download these files (yet) - you need to log into iCloud to access the files even if you can "see" them in iCloud on your iOS device.
There are some key differences you should be aware of between the iOS and OSX versions of Keynote:
- not all animations, actions and builds created on a Mac are supported on iOS
- the iOS set of available fonts is limited and not expandable, at this point, so some fonts used on OSX will be replaced by iOS Keynote
- you may find timing of some actions a bit off and need tweaking
There is an article on best practices when using Keynote for iPad that is worth viewing:
http://support.apple.com/kb/HT4114?viewlocale=en_US&locale=en_US
Hope this answers your questions.