Slow down as you come to a tree. Release the automatic forward motion bar and move it yourself. This gives you total control of the mower and reduces the risk of damaging the tree.
Mow with the grass spreader away from the tree. This allows you to get closer to the tree without slamming into it, and you can turn around the tree much tighter.
Remove the grass around the tree to make mowing easier and to protect your tree. You can cover the soil with mulch or other ground cover, or just leave it as is.