Just to be clear, there is more then two methods to update Joomla. I just want to show two most common. Sometimes you will be forced to use some other method.
Recommended method is to use built-in updater on Control panel. All you have to to is to login to administrative backend and select Update Now button (Slide 1).
Second method is to do it using traditional way: uploading file to home installation directory. Before you do it, verify which Joomla version you run and then from Joomla Download page, download accurate update file.
On Control Panel page, select Extensions – Manage (Slide 2).
On next page you will find traditional uploader. Select Browse and choose file you downloaded from Joomla site (Slide 3).
Next step is to select Upload & Install button (Slide 4.). File will be uploaded and installed. On finished installation you will be logged out.
Now you have to check is your system updated. Go to Control Panel and on bottom find relevant information (Slide 5.).
Perform your updates regularly, due to fact that Joomla (alog with other open source CMS`s) is vulnerable. Keep it updated, thus safe.
I hope that this tutorial was informative to you and thank you for visiting this website.