The simplest way to add images is to upload them from your computer using the Media Manager. First, of course, you have to download the image onto your computer and be able to find it. Then, from the Control Panel (back-end administrative interface) navigate to Site -> Media Manager.
On the left is a directory tree, with the root directory "Media". This corresponds to the default "images" directory, yoursite/joomla/images. Pick a subdirectory where you want the image located, or else do nothing to upload the image to the default images directory.
At the bottom of the page is a typical Upload box. Click "Browse" to locate the image on your computer, then "Upload" to upload the file to the server.
Of course, you can upload images to a server using any standard FTP client. You might find this handier for adding images to template directories; however, if you have FTP set up, you probably don't need an explanation of how to add an image. Also, many server administration panels such as Cpanel and Plesk have upload capabilities.
There are several extensions, available from the Joomla extensions section, that handle image uploads.