At the back of the lobby there is a fishing area which is the only place you can use a fishing rod at. Once you equip a fishing rod you can go next to the lake and dip the hook underwater by holding left click.  
After a while you will feel a fish biting your hook and can now reel your catch in by holding right click and press E to put the catch in your inventory.  
Rarity of rod will increase the depth of how far your hook can go down, the deeper it goes the higher chance at finding higher rarity fish or item becomes!  
You have a rare chance of finding mystery bait which can be combined with a mystery skull for a special boss skull.