I like to lay a few limbs/firewood pieces perpendicular to the direction of tree fall and let the trunk rest on them. That keeps the log off the ground and the saw out of the dirt. If that's not possible, then there is almost always a spot on the trunk that is off the ground every few feet, and it's just a matter of cutting through at this point so that the cuts can be made from the top, piece rolled, and the cut finished going up. Simple takes a bit of practice to get good at it.
Best reply yet, it takes about 2 seconds to dull up a chain in the dirt. I told my dumb BIL to keep the chain out of the dirt, then I'd watch him put the tip 3 inches in the dirt, he'd never get more than 20 minutes out of a chain. Steve