Using a large, deep skillet, add olive oil. Allow to heat over medium. While oil heats dice onion, peel and dice sweet potato, and slice sausage. Set aside separately.
Once oil has heated, add onions and cook until they become translucent. Add sweet potato and cook for 10-15 minutes, or until they begin to soften.
Add sausage and cook until no longer pink. Turn heat down, add kale, and toss to coat and heat thoroughly.