Everyone starts with 2 Shuttles.
In the Faction mission screen, when you see Shuttles 0/2 it means that you have 0 shuttle on a mission, and have 2 available to send on a mission.
Using a transmission will let you choose a crew for the chosen mission, and once you start it, the shuttle count will display 1/2.
When you select a mission, you have to select your crew within the specific time allotted. After pressing start, the time displayed is how long the mission will last until it can be completed.
Once a mission is finished, click Complete to see the results.