The orbital command was introduced in Update 7 and its overall level is shared throughout a faction, similar to faction research. However, the launch building is given to everyone and can be upgraded, it is located in the upper left of your base. At level 1, you can launch a rocket every 24 hours. The building maxes out at level 10, but you need to have headquarters at level 30. Each upgrade reduces launch time, and maxed out you would be able to launch every 12 hours.
Each launch requires resources, medals, hearts, or intel, depending on the rarity of the reward you would be getting. Since the rewards are not very good, I would suggest only launching with resources. Each launch gives core energy (mostly useless) or construction materials (this levels up the command for the faction).
The easiest way to get this achievement to find a faction that is somewhat active and contribute by launching as often you can. If you can get into one of top factions in your world, then that would be the best case scenario. It has taken my faction about two months to get to level 15 orbital command and we are very active.
From LordMakanaki "Also your rocket needs to be level 2 before you can launch."