Ok so Matron is a gathering mission, you switch to a DoL when you enter and your mission progress bar is advanced by simply hitting nodes. Fury is a battle mission in which you're directed to certain enemies and otherwise participate in Fates until the next mission is available. Upon completing your 3 missions you receive a loot bag and are then free to access additional areas if you want to fight Notorious Monsters or gather from unspoiled nodes. If the weather changes to hyperelectricity then a portal opens to a raid area which is impossible to clear without a large amount of players.

Entry via Ishgard requires 8 people in the matchmaking queue and likely won't ever happen. Entry via FC workshop airships requires just a minimum of 2 people each holding mission ceruleum and you can clear a Matron mission slowly like that. Upon entry you start at one of 9 possible landing pads (maximum 9 parties = 72 players per instance when it was popular). It used to require aether currents but nowadays you can fly immediately and map the area achievement if you want to.