What platform is this on? What hardware? What O/S?
Generally, you run some cluster/DR suite of software that manages failover. In those situations you might have node A and node B clustered. Node A is the production box and node B the DR box.
Both node A & B would have their "hardwired - never to change" IP addresses and the cluster suite presents a pseudo ip address to all clients. The clients only ever access this pseudo ip address (and don't know about the real ip addresses). When failover occurs the suite moves the pseudo ip address to the other node and the clients are none the wiser (apart from perhaps a few seconds hang).
This is very similar to what HACMP (IBMs failover software for AIX) does too. In HACMPs wording what you call "pseudo IP" is called "service IP" and technically it is an IP alias, which is moved with the "resource group" (a group of mounted file systems, start-/stop-scripts for the application and said IP address(es)).
There is not so much "to do" - of course you can write such a high-availability system yourself. We will talk again a few years from now, probably....
What you have to do is to install such a high-availability software and form a cluster. There are several such software out there: HACMP, Veritas, Beowulf, NonStop-Cluster and probably a few dozen others. As you mentioned you run on Itanium i assume you have HP-Ux as OS, so you will probably need to install NonStop Cluster from HP.
I suggest you read up about "Failover-Clusters" and "active-passive clusters", as this is what you describe.