Since this word consists of a kanji with hiragana attached, you can bet that it will use the kun'yomi reading. You didn't learn that reading with this kanji, so here's a mnemonic to help you:
Before you start to spin you have to let out two moos (つむ) as tribute to the cows that gave you their fur to make yarn out of. Go on, two moos, right now. Hey, out loud, not in your head!
A long time ago thread was spun in this way.