Apple's Time Machine backup service in OS X supports options to back up data to locally attached drives, or to networked drives such as Apple's Time Capsule devices. In addition, you can configure Time Machine to back up to a share point on another Mac. For instance, if you have a large 2-3TB USB drive attached to a desktop Mac, you can mount this drive on any other Mac as a shared folder, and then use it as a Time Machine backup destination.
This setup should provide you with networked backups, without needing to purchase a separate NAS device; however, if you use the Back to My Mac feature in iCloud, you might run into difficulties with this specific setup.
Generally, to associate the share with Time Machine, you simply select the network server in the Finder sidebar and after authenticating, you can click a share point. When mounted, the share point should appear as a destination option for Time Machine. However, you may find when doing this that the share will simply not show up as an option for Time Machine, even though it mounts properly in the Finder.
If you run into this situation, the issue may be that you are using the Back To My Mac service, which establishes a connection to your systems via iCloud. Therefore, if you find your network shares not appearing for Time Machine when mounted, try unmounting and remounting them directly using the Connect to Server option in the Finder's Go menu. In the address field, enter the computer's IP address or Bonjour network name, which should ensure that the connection is established through the local router instead of any other means.
Now when the networked share is mounted, you should be able to associate it as a Time Machine backup destination.