Every faction aboard is recruiting. Visit their headquarters in the Port of Call (the Saja recruit at the Shrine of the Whills), hear their pitch, and choose the Missions you want to run.
Each passenger receives Mission Tokens at check-in. To join a Mission, trade one Mission Token for one Mission Pin for a specific run. Each run has a limited number of Pins: when a faction runs out of Pins for a run, that run is full. Your Pin is your place at that Mission's briefing, so bring it with you. Tokens and Pins can be traded between passengers.
Once you have your Pins, log them on your Profile so your Nav can remind you where you are expected.
Spend your Mission Tokens with any faction you like. But come Saturday evening, every faction gathers at once, and you will have to choose just one.