Here is a short video to demonstrate this on how VMware High Availability (HA) test is conducted and configured as stated in this KB. Do note that only vSphere 5.x methods are shown in this video.
Many I have spoken with is still unclear how HA really works. You can refer to Duncan Epping's post here on more deep dive of HA.
HA is enabled from vCenter with just a simple checked box. Once that is enabled, the ESX servers will have a HA agent (FDM) running and this will communicate within the ESX servers in the cluster and with one of them as the Master role communicating with vCenter. In vSphere 5.0, in the new HA architecture, there will be one Master node and rest as salves nodes.
In vSphere 5.0, datastore heartbeat was introduced on top of just relying on the traditional management heartbeat. i.e. to say, if a ESX server lost it management heartbeat with the rest, as long the datastore is still alive with VM still running (If ESX server has failed, there will be no heartbeat), Host Isolation>Virtual Machine Options will follow the policy that is set. This creates a 2nd safe check in case of a failure.
So in summary if you have set Virtual Machine Options as Leave Powered On, host isolation will not trigger failover but leave the VM running on the host as the host still lock on to the VM files. However if this is set to Shutdown or Power off, VM will failover to other host as the lock on the failed ESX server is released. This KB explains the above in detail.