There is 2 types of IP fail over:
- DNS level
- Server Level
DNS Level - Failover
A DNS fail over can be setup using online DNS IP failovers but they cost money and many people say they are not as good as doing it on the server level, since at DNS level they check your hosting on intervenes and these can be from 4-10mins at any time. A Quick Google search reveals DNS Failover System Monitoring.
Server Level - IP Failover
It's highly doubtful you can do this with standard shared hosting as you do not have access to setting up a IP fail over procedure.
Normally you would proceed with the following:
- Replicate Clone of MySQL on both Servers
- Clone the file systems using clusters
- Interment a IP fail over using something like UCARP
But Why Shared Hosting?
If you are serious about up time then shared hosting is not the most ideal hosting to get since interment downtime can occur from the result of other users on the hosting. Never mind that shared hosting generally is much slower than dedicated and VPS hosting, as well as not being as secure.
If you want the best up time then your better of getting a VPS on a cloud such as Amazon EC2, or Rackspace Cloud Server as well as using Anycast DNS or better.