The Teleporter and Teleporter Cores are new blocks and items that can be obtained after reaching the End Dungeon in the Stalwart Dungeons mod. By combining them together, you can travel between different points within the same dimension.
Crafting the Teleporter Core
A single Teleporter Core can be crafted from 1 Ender Pearl and 1 Void Crystal. When killing the Shelterer, located inside the End Dungeon, it will drop 4 Void Crystals each time, and that’s the only way to obtain them currently.

Only one of these are required to operate Teleporters. Though for maximum efficiency, and to be able to teleport to a place and back, you’ll want at least two.
Crafting Teleporters
To use Teleporter Cores, at least two teleporters are required. And two of these can be obtained by placing 8 Purpur Bricks and a Void Crystal inside a Crafting Table.

Purpur Bricks are a new item included with Stalwart Dungeons. They can either be mined within the End Dungeon, or created by combining 4 vanilla Purpur Blocks. So you might want to kill the Shelterer multiple times to obtain the most Teleporters and Cores.
Using Teleporters
Now, Teleporters can be placed inside any dimension, but you can only teleport between them within the same dimension. So teleporting from the Overworld to the End isn’t possible, but teleporting between two points in the Overworld, or two points in the Nether is.
Make sure you have two Teleporters and two Teleporter Cores in your inventory before proceeding. Place down one Teleporter in your house, and sneak and right click it with a Teleporter Core. You should hear a slight Anvil sound, and when hovering over the Teleporter Core, it will show that coordinates have been bound to it.

Place the other Teleporter in a location that you wish to teleport to. This could be a few blocks away for testing purposes, as you can always mine them later. When placed down, sneak and right click it with your other Teleporter Core, so that the destination is saved.
Now regularly right click the Teleporter, and add the Teleporter Core that is bound to your house. When placed inside, you can stand on the Teleporter and sneak, and you’ll be teleported to the location stored inside the Core. Then place your other Core in the Teleporter you just teleported to, and you can go back and forth.
It sounds quite confusing, but it’s simple. Standing and sneaking on a Teleporter will cause you to teleport to the coordinates stored in the Core within it.