Starfield

After joining the Constellation, you will be asked to go speak to Commander Tuala. He is at the entrance of the MAST District building (the big one that has MAST in big letters) behind not the first counter, but the one to the left where it say Vanguard on the wall.

At this point you can start the 'Supra Et Ultra' mission by selecting the correct dialogue options.

Take the elevator down and make your way over to the end of the museum. Interacting with all the museum dialogues is optional but quite interesting.

At the end you will then need to pass a pilot test and make it through 3 tiers of attacks. Once done, you can then go back up to Commander Tuala and complete 'Supra Et Ultra'.

You're not done yet - now you also need to complete the 'Grunt Work' mission which will now trigger and be in your mission log. Fast travel over to the New Atlantis Spaceport and speak to Chief Kane Herath.

Now travel on over to Tau Ceti to kill a Terramorph. At first I tried to kill the Terramorph outright without doing the optional objectives. I recommend doing the 3 optional objectives as it will turn on a turret system.

After killing the Terramorph, travel back to Commander Tuala to complete 'Grunt Work'. Achievement will now pop after speaking to Tuala.

Once you have joined constellation, you will be tasked with talking to a person.

Once you have walked through New Atlantis to your location and have started talking to the NPC as part of the questline, you will have the dialogue choice to join Vanguard.
Select this option, complete the practical test down the elevator and then complete the probationary quest to be recruited into the Vanguard.