Default: The default way of getting to and from The Wilds can be discovered by exploring the server's main town or asking other players.
Custom Portals: Players can also build their own custom portals. See the linked page for more info.
Expanding the border will unlock more of the unique things about the Wilds: Land to explore, new mobs and their respective drops, new bosses, new structures and dungeons, and more information/lore about the Wilds. An additional bonus is that you can also create portals to the Overworld that are even further out, which is good if your Overworld base is far away or if you'd like to fast travel vast distances faster than the Nether.
Consider this the “Phase 1” mechanic. The requirements may change for future expansions. Note that ALL of the requirements below must be met before the border will expand. These do not need to be done in this exact order.
Establish a settlement in the currently-accessible area of the Wilds. This needs to be something like a village, town, outpost, castle, etc., not just one building/house. This is meant to be a safe area for players in that zone. You can create your own settlement or help others with theirs, your choice. It doesn't need to be a large settlement, it just can't be a single building like the safehouse.
Map the currently-accessible area of the Wilds using regular Minecraft maps and form a map wall. This can be a group effort (like the Explorers Guild and other groups), a lone wolf exercise, or multiple groups cooperating - it's up to you. However, the map wall must be inside of a settlement. The COMPLETE map wall must be in ONE settlement, not spread out across multiple. Will you cooperate with others and combine your maps, or spend extra effort to do it all yourself?
Create infrastructure from the settlement (the one with the map wall) to the current Wilds border, in any direction, and it does not have to be a straight line. This can be a simple path, a larger road, a rail, etc. Note that future settlements will need to connect back to prior settlements, like connect-the-dots.
Discover the major dungeon in the area and defeat the boss there. You will know it's the right boss because it will have an actual boss bar; minor bosses will not have this.
Create a monument representing one of the boss' unique drops, and place that drop in an item frame somewhere on the monument.