There is a simple to use teleportation system in Fine Technology. To get started with it, you will need to collect a lot of soul sand and some iron blocks.
From them you can craft Teleporter Components - blocks that a teleporter consists of. For each teleporter you will need 9 Components. Then you can build a teleporter frame - vertical or horizontal:
Then put the last block in the center of the frame, and it will create a teleporter:
Then right click the central block, and it will open an interface:
Here you can set this teleporter's channel. After setting teleporter's channel, make another teleporter and open its interface.
All other teleportation channels will appear automatically on the right side. Set this teleporter's channel. Then test teleportation by pressing respective channels' buttons. The position of teleportation is determined at the time of last block placement - it will be offset in direction to player.
You can set a destination for entities that collide with the center block by Shift+clicking the target channel button. Colliding entities then will be able to teleport to specified 'collision destination'.
Remember that these teleporters don't work across dimensions (but may be in the future).