Before starting it always is wise to read the documentation associated with an extension. Most extensions have homepages and forums, and it is a good idea to look at them first. If there is a README file included with the extension, you should read it.
For most extensions and most users, the procedure will be:
Download the extension to your local machine as a zip file package.
From the backend of your Joomla site (administration) select Extensions → Install/Uninstall.
Click the Browse button and select the extension package on your local machine.
Click the Upload File & Install button.
Some extensions may provide further instructions on installation.
Note that modules and plugins must be enabled before they will work.
There are some situations in which this procedure will not work.
Sometimes you need to unzip the file locally prior to installing. If you get an error saying that the file is not in the correct format, the need to unzip is a common cause of this. After unzipping try installing the individual items. Note that the files you upload using the installer still need to be zipped.
Sometimes you cannot use the automated installer. For example, very large extensions may exceed the maximum upload size allowed by your host.