If you opt for a concurrent user license then you can install SPSS on as many machines as you like, as long as it is only ever used by one person at a time. To control this you would install SPSS License Manager. The license manager is a separate application which will need to be installed on a central machine/server to host the license.
Once the license manager is installed and license is added, this machine will have a background service running (at all times as long as the machine is on) that will host the licenses. Each end user then needs to point their software to this machine (either the IP address or server/machine name).
From then on, every time the user opens SPSS Statistics they will automatically retrieve the license to run the server (providing no one else is using it at the time). The end user can also use the Commuter application to check out a license in case they want to use it outside the network (for instance a laptop user who wants to take continue working out of the office).
To ensure the license is always returned there is a time limit which will automatically return the license to the license manager.
You can download the full IBM SPSS installation guide as a PDF here.