SAS can be run in client-server model, using either the Enterprise Guide thick client or the SAS Studio thin (web-enabled) client, or in "local server" mode where a fully functional SAS system is present on a local machine (Windows or Unix/Linux desktop or server running in interactive mode) and run either in Display Manager mode (the local client) or through one of the client-server clients above (connected to the locally installed server).
SAS installation typically is performed by a SAS administrator, who will install the software from a software depot that is customized for the site (and often provided by SAS Institute directly).
For the purpose of learning SAS, there is also the free SAS University Edition, which can be installed for free for educational purposes by anyone on a Windows, Mac, or Unix/Linux computer. It is available from SAS directly, currently at the SAS University Edition page, either by running an AWS instance (on the free tier) or by downloading a virtual machine locally. See the installation guide on SAS.com for up to date instructions, or below for the current (July 2016) instructions.
To install it locally, you first download and install Oracle Virtualbox 5.0 (Windows/Mac/Linux). Then download the newest SAS University Edition disk image, which is around 2GB and requires setting up a SAS.com profile.
Once you've done so, you need to set up the virtual machine in VirtualBox. Import the SAS VM as an appliance ("Import Appliance" in VirtualBox). Create a folder for SAS to use as its local storage (so you can put files in a location SAS can see them), and set that up as a Shared Folder in the machine settings dialog box. Set it up to auto-mount.
Then, start the SAS virtual machine, and once it's started you can connect via your web browser, connecting to http://localhost:10080/ if you used the default settings.