Trick #1: Avoid Tangling Yarn by Using Containers
I like to put my two different balls of yarn into different containers. You can use yarn bowls if you want, but a couple colanders or food storage containers with the yarn fed through the steam vent also works. The two containers will prevent the balls from rolling all over and tangling more than necessary.
Trick #2: If the Yarn Keeps Tangling, Don’t Fight It
Let them tangle. No, seriously. Sometimes, the easiest way to deal with tangling is to let it happen and periodically untwist your work using the force of gravity. This method only really works if you're knitting smaller projects, like socks, but it’s not so great for sweaters.
Trick #3: Keep the Yarns on Separate Sides of Your Body
Keeping a second ball of yarn on the other side of your body can help keep them from tangling a bit. You’ll still have to untangle the yarn periodically as it twists around itself when you’re working, but you’re not going to have the balls tumbling and rolling over each other and getting more tangled while you work.