In basic terms:
- You have two or more load balancers running at the same time
- They are both configured with the same config, IP address, etc
- They run a heartbeat
- Only one is active at any given time
- When the heartbeat from the active node goes away (fails), the rest negotiate between them who will come online next
Basically high availability in an active/passive cluster works the same way nomatter which technologies you're using, so the above applies for Load Balancers, Database Servers, Hypervisors, etc.
In Linux this is done with a combination of tools, one of which is actually called heartbeat (and syncing your configs is often done with drdb).
In Windows, you would generally use Failover Clustering, or Network Load Balancing, both of which offer a virtual IP address shared by multiple servers. Syncing your configs can be done with DFS-R for Network Load Balancing, or clustering actually has the ability to share a registry hive and re-configure it in the case of a failover.