Instructions
Buy a yarn maker. The yarn maker is for sale at the General Store and costs 4500G. You will receive the dying pot free when you buy the yarn maker. You need the dying pot to make red wool yarn.
Raise sheep or buy wool. You can buy a lamb from the Brownie Ranch for 4200G. It will grow into an adult sheep in 14 days. An adult sheep produces wool every four days. You must buy shears from the Brownie Ranch for 1200G before you can get the wool from the sheep. You can buy decent wool yarn from Simon during the Spring Flea Market on Spring 22. This readymade yarn will cost you 375G. You also can buy good wool yarn from Hannah for 465G on Spring 28 at the Animal Festival.
Process the wool with the yarn maker if you opt to raise your own sheep. Stand in front of the yarn maker with the wool in your farmer's hands and drop the wool in to get wool yarn.
Grow or forage a red herb or a red flower. You need a red plant to dye yarn red. You can find red herbs throughout the town and forest year-round, although they grow in different places and you're not guaranteed to see one every day. You also can grow red herbs. A red flower also will work to dye the yarn. In spring, grow tulips. In the summer, grow hibiscuses. You can grow either cosmos flowers or roses in the fall. In winter, grow anemones.
Put the yarn and the red herb or flower in the dying pot to turn your wool yarn red. Stand in front of the dying pot and choose wool yarn and a red herb or a red flower from your rucksack. You will now have red wool yarn.