The cluster network handles failover.
You can setup a cluster without shared storage, that doesn't make it recommended, but it can work. You still need to create the cluster networks as needed. In this case, the transfer of things like VHDs and other files will transfer over the cluster network during a failover.
This isn't really a high availability cluster, though. Failover time will depend on the size of the servers being transferred and the link speed between the server. This also won't function as a decent disaster solution as one server going down likely won't have enough time to fail the servers over.
Keep in mind that even though the cluster is not using shared storage, it still needs to have some storage available to it. Otherwise, you won't be able to fail over storage dependent resources (such as virtual machines). You can add storage by selecting the Disks container and then clicking on the Add Disks link.
As you can see, it is relatively easy to set up failover clustering. The entire process can usually be completed in less than fifteen minutes.