If you go to a vendor (such as the ship component vendors at Sol) there will be a menu option that says "How do I purchase items from you" or something to that affect. Click that and it will tell you what order of explore merits you need and in what areas of space you'll get them.
Lt. Grall usually hands those explore missions out when you reach high enough level. I'm currently Lt. Cmdr 1 but still getting the Delta Volanis and Arucanis ones.
I believe he hads out all the exploration missions, as soon as I leveled to lvl 13 last night i recieved a new sector exploration mission from him. I believe he works that way once you are in level range, like Sulu does when you reach patrol range for a given sector and hands you the patrol mission.
When you hit the appropriate level one of the guys at Starfleet (not Grall) will give you a mission to go to the cluster and get the mission from Grall. Once you have that and go to the appropriate cluster you'll get the first exploration mission, which then becomes repeatable. (I think I was LC 2 or so whenI got Hromi.)