Nimbostratus
Cirrocumulus
Firstly failover. To do this either from the cli run b failover standby or in the GUI go to High Availability and select Force to Standby. The Redundancy State Preference is there in case you'd rather one particular LTM always be the Active appliance, however, this can cause multiple failovers as once a failed Active that goes Standby is back online and set with a Preference of Active it will force a failover back so it's back to Active.
As for the failover and connections, there are two options for you Connection and Persistence Mirroring. Both disabled by default, Connection Mirroring has a high overload so not always desirable, however, I'd recommend Persistence Mirroring - i.e. in the case of a failover a client will go to the same pool member (as the Standby is aware of the persistence record). No need if you're using http and cookie persistence though - the client is in control here.
Hope this helps.
N