Some people just delete the theme (from the WP admin themes page) and then reinstall. If you want to do it this way, just Activate another theme (like the Genesis Framework for example), then delete the Ally theme and install the new version. Make sure and back up everything (database, theme files, etc) just in case an error is made.
If you have FTP access then I would recommend updating/replacing the files that way instead. It’s the way I and most developers do it when replacing theme files.
The slider should be fine since it is a separate plugin. Although there is also an update to the slider which should be included in your account as a separate download. So you can update the slider as well if you’re interested.