In order to set by an irrigation system, you need two special items; the Irrigation Flooring and the Irrigation Tower. Both of these can be bought from the Church Store, where the tower cost 10x Data Discs each, and each Irrigation Floor cost 1x Data Disc.
You will need one tower and up to 8 Irrigation Floors for a basic set-up, but you can start off with one tower and a few floors and work your way up as you get more Data Discs to spend.
How to set up the Irrigation Tower and Irrigation FloorsSet up the Irrigation Tower in an area in your Workshop where you have enough tiles to go underneath each planter box you want to use. Place Irrigation Floors in a 2x2 grid where you want the Irrigation Tower to be, and cover the area around it with Irrigation Floors where you want to put your Planting Boxes. Keep in mind that all the tiles below a Planter Box must be filled with an Irrigation Floor to be irrigated.
Connect all the Planter Boxes with Irrigation Floors below them by using Irrigation Floors as a pathway. This is not needed if the Planter Boxes are directly next to the Irrigation Tower, but it's important that they are connected, or else it won't work.
Now just fill the Irrigation Tower with Fertilizer using your left mouse button, and it will gradually fill up. You will to restock it with new Fertilizer once in a while, but it's not that often really.
And that's it! Enjoy your extra produce from the irrigated and fertilized crops.