Heard of 'clicker training'? It's basically applied behavioural psych with positive reinforcement. Google it for more info, as whatever you want to teach, understanding the principles behind it will help you.
Fetching; first you teach the horse to touch something on cue - say your hat(use an old one you don't mind scuffed & slobbered on!) Once he's reliable at touching something whenever you ask, even if it requires walking to, then you can start asking him to mouth it. A shortcut to this stage is to hide a few treats in the hat! Then teach him to hold it in his mouth. Then teach him to 'give' it to you - I also start this with a lure - when he's standing with it in his mouth, I distract him with Something Extra Good so he looks/puts his head near me. Repeat this until it's solid without a lure and then gradually increase the distance he is from you when cuing.
PS I don't attach a vocal cue to the behaviour until he's got the gist of it & is reliably picking it up, to ensure he associates the cue with the right behaviour - I say 'Get it' to pick something up, 'Give' for him to bring it.