This guide aims to explain the general flow of the Matter Board. It won’t tell you how to do specific Matter Board quests.
The Matter Board itself will actually pop up automatically when you return to the Camp Ship or Arks Ship upon completion of its current objective. If you’re already on the Arks Ship (because the node’s objective is to talk to an NPC for example) the Matter Board will pop up immediately after you’re done.
The “nodes” on the Matter Board are arranged into a grid, with the origin being in the top-left corner of the board. Each node is labelled after its position on this grid. For example, the currently selected node in the above picture is “B-2”. When using Matter Board guides, this is how you reference a given node.
You can only select nodes that are directly adjacent, vertically or horizontally, to nodes you have already completed. Selecting a node will indicate which nodes will be unlocked upon completion. To pick one just click and press the left button in the window that pops up. The Matter Board quest will now be active.
Most Matter Board nodes are blue and generally require you to find an item in a given quest. The specific quest and area are specified in the bottom right window in the above screenshot. That’s the information you will need to concern yourself with if you are aiming to complete a node.
Generally speaking, you will want to just match the quest name to a mission you can choose at the Quest Counter. A tutorial for starting quests can be found here. Below the quest name is the area (エリア） of the quest you will need to be in.
For the large part, Matter Board quests can just be completed passively. The drops for the board are of course random, but you will know when they happen because they will play a different sound effect and be a light golden colour (no matter what the item is).
For orange nodes, the objectives are different. In the first Matter Board at least, you’re just required to speak to NPCs. I’m afraid there are no visual indicators, so the best you can do is either try to match the Japanese text to an NPC’s name in the lobby or wait for a guide to direct you. You could always just brute force it and try every NPC in the lobby, of course.