How do I set up active-passive database clustering between data centers?
So you've got a couple of options when it comes to doing this.  

Option 1: Use a geographically dispersed cluster which is a single cluster deployed in both data centers.  This gives you one single cluster which exists in both sites.  You would end up having several nodes in each site so that when doing local site patching you don't have to fail over to the second site.  In the event of a site failure you would then fail the cluster over to the second site.  To change to the clients would be needed as they would just connect to the same virtual name which would then resolve to a new IP address.

Option 2: Database Mirroring between sites.  This is the preferred option as it's easier to setup, doesn't require expensive SAN replication software, and failover and back is all handled via SQL Server.  I'd recommend a two node cluster in each site for local HA, then mirroring between the sites for your DR setup.  Local HA covers server patching which the database mirroring covers you for DR.  If the sites are far from each other setup the system with asynchronous mirroring, if they are close to each other the you can use synchronous mirroring which will allow for no data loss.