The Master Sword is unique in that it's the only unbreakable weapon in the game. Its durability wanes with use, but after a few minutes recharging in your inventory, it's good to go again.
It's worth finding the sword as it does double damage against Ganon and his minions.
The Master Sword is tucked away in the middle of Korok Forest, to the north of the castle.
From the ruin at the woods' entrance, follow the path of torches until they appear to end, then head west to find a pair of torches next to a large tree with a chest inside.
Pick up the torch on the ground and light it. Watch the direction of the falling embers and use them to navigate the rest of the way.
You'll be invited to pull the sword from the stone, and as you do, your heart gauge will deplete, but it will replenish immediately afterwards.
You'll need at least 13 hearts to yank it free, so get to completing shrines for Spirit Orbs, and defeating the Divine Beasts, stat.