On occasion, you may receive Transmissions from other factions requesting aid. While you must attend to your Starfleet duties, you can send a team to assist them remotely via Shuttle missions.
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. You can invest in additional Shuttle Bays to increase your capacity for responding to such Transmissions.
Activating a Transmission will allow you to view the briefing and requirements for the mission. You will have up to 12 hours after activating the Transmission to confirm that you will be taking it on by assigning it Crew and sending them to the mission location. You should select Crew who match the requested Skills, but be aware that you will not have access to those Crew members until they return, so you may wish to select Crew that you don't forsee any firsthand work for in the immediate future.
Each Shuttle Mission has a duration, which is stated when setting up the mission, and a success chance, which is dependent on the Crew that you assign. You can apply a Shuttle Boost to reduce the duration, or to enhance a Skill used for the mission or the Rewards received. Note that improving the Rewards also increases the duration, and is best used if you anticipate not being able to check in for much longer than a typical Shuttle Mission would last to maximize your Crew's productivity while you're away. Ultimately, no matter how well you stock your mission, it's always possible for something to go wrong, so don't be too hard on your Crew if what seemed straightforward ends up being a lost cause.
Once a mission is finished, click Complete to see the results. Successfully completing Shuttle Missions will increase your Reputation with the Faction that made the initial request, so it's a great way to curry favor and improve your standing in diplomatic affairs. It may even make certain Factions predisposed to offer you better deals on supplies.
Shuttle Missions become available at level 5, and an be accessed via the bottom button depicting a shuttle.