How to update
There are two ways to update a theme. The regular and auto way.
This is the easiest way to update a theme and it is controlled by the theme options (please read the manual for more details or simply go to the theme options panel). Most themes come with a field in which you put your Buyer Username and API Key (not password!). By completing these correctly you should be notified in your WordPress dashboard as soon as an update for the theme appears.
Att: This feature might not work on absolutely all environments (i know for a fact that it doesn't work at all in WPMU for example). So if you see that it's not working, it's not the end of the world, but you'll have to update manually as explained below.
If the theme uses plugins and there are updates available for them, you should see a notification and be able to easily install them. However, if you don't see the notifications or aren't able to autoupdate, you can update the plugins manually as well (plugin zip files are in the theme's-folder/includes/plugins).
To update a plugin manually you can simply remove the plugin from your WordPress dashboad (deactivate and delete), then install the new one from the dashboard by using the archive from the theme folder.
Make sure that you do not edit the theme files! If you have custom CSS code, insert it into the Custom CSS Panel in the Theme Options > General area. If you also want to modify PHP files, then please use a child theme.