You'll need the quest to fix the nets first. I think Yotra (smith) gives it to you after some resource gathering quests.
You'll need 3x nettle and her workbench in her house (Right next to the smithy.)
She should also give you the recipe for nettle thread.
The recipe is a bit misleading, mentioning a third part of nettle (Leaves, Stems and something not existing).
Just place 3 nettle stems on the crafting menu and work it with the hand tool. This creates a ball of yarn.
Next place the broken net and the yarn into the crafting menu and use the needle tool. (Check order of items in recipe!)