You just need to speak to an NPC, it's not an actual quest or anything.
In Limsa it's Ursulie
In Ul'Dah it's Thaisie
And in Gridania it's Gyles
You just talk to them, choose the race, and then they show you a selection of different retainers. You can choose their name after you've made your selection. They all do the same thing, but have slightly different personalities. Some act like they're five years old, some are a bit religious, some just want to get paid and go home, etc. If you just want to store stuff, just choose whichever. You may need to be at a certain point in the story quests, but if that is actually the case you don't need to be very far in at all.
All of these are in their respective cities Adventurer's Guild by the way.
I have no idea why Gridania is called the Briefing Room here. That makes no sense to me at all. Edited, Oct 7th 2011 7:55am by Uchitoru