Please note: It’s recommended that you make a backup of the theme prior to updating. BackupBuddy is recommended to backup and restore your whole site.
From your WordPress dashboard, navigate to Themes. Activate a different theme, choose delete files for your theme, then upload the new theme and activate.
It seems scary but you really won’t loose any of your data. The only exception is if you have made edits to theme files like header.php, footer.php etc. These changes will need to made again to the new files. But all of your content and theme settings are preserved.
Alternatively, you may want to use a plugin to automate backing up your current theme and uploading the new version: http://wordpress.org/extend/plugins/easy-theme-and-plugin-upgrades/