I currently have a couple vmware esxi servers with a data store using the server's local hard drives. I am going to set up a NAS server that will support NFS or iSCSI. I would like to mount that on the VMWare server and move the current datastore on to it. Is this possible, and basically, how?
Sure - but it can only be done with the VM running of you have licensing that allows for Storage VMotion.
Otherwise, you'll shut the VM down and unregister it ("remove from inventory"), then in the datastore browser select the VM's directory and select the "move" option (the little paper with an arrow) in the top panel. Once that completes, find the VM in the new location in the datastore browser, right-click the .vmx file, and register it. When it's booting, it'll ask whether it was moved or copied; select moved.
If your task is to move content of the datastore to the new LUN then shutting down VMs, unregistering them, and copying files using vsphere client ( or any other apporpriate method) from old LUN to new LUN , then reregistering VMs using .vmx files again.
If you cannot afford a downtime, the process becomes more complicated and depends on your requirements.
In clarification of Shane's answer - you would need to have a vCenter Server in order to do what you desire (without the need of manually moving files between the data stores).
My clients had independent ESXi instances in place and then opted to move their data to a SAN. If you don't want to deal with downtime (and you don't have an existing vCenter license) I would suggest trying out the free demo - it allows for free live storage vMotion for 60 days if my memory serves.
It also helped to convince my clients to go with a full vCenter install. :)
EDIT - This was for the 4.1 release. Not sure if things have changed that much for 5.