They cannot be crafted by the player, only purchased in shops or from NPCs. They are very inexpensive, costing about 9 torches, or a single empty wooden tub, or a couple cords (this information may be outdated).
Fishing with a fishing rod is a restful activity and can be used as a somewhat more productive way of reducing fatigue than simply waiting.
During the 'Fishing' part of the Living in the Wild tutorial course, the player automatically receives a fishing rod for free. He or she can keep the fishing rod after the 'Fishing' part of the course concludes.
This makes the whole game course very welcoming to new players of URW, who need a dependable enough food source at the start - fishing with a rod being one of the best regular food-gathering techniques before the player character has settled and built-up enough to have a guaranteed steady source of food from picking, agriculture, fishing and hunting.