GTM provides 'smart' DNS responses - this is generally either datacentre failover or anycast. Datacentre failover involves the GTM monitoring the devices in multiple datacentres and if one datacentre goes down then it responds to DNS requests with the other datacentre. Anycast involves responding to DNS requests with the closest datacentre eg users from Europe go to the London datacentre, users from China go to the Beijing datacentre.
This is done with the use of WideIPs, which are FQDNs mapped to different datacentres, etc. A datacentre can contain LTM-type objects and links, etc.
Bear these things in mind and reread the documentation and try setting it up.