How can I keep my yarn relatively stationary while working?
Yarn Bowl



This is the easiest suggestion I can think of. You just need a bowl or bowl like object with a hole or path for the yarn to come out. The hole is large enough for the yarn but small enough to stop the ball from moving around. The weight of the bowl is important as well since you will be pulling on it. Having it close to yourself would help that anyway. 

There are oodles of commercial options but avid crafters would make their own following the basic criteria above.