Just get up high and push them over. Some trees, you may have to dig up the roots opposite the side in which the tree will be falling.
To elaborate a little on what rino says...I always try, as much as possible, to
leave the roots undisturbed, on the side away from the machine. The reason is that, those roots won't really support the tree against falling in that direction, but, if your bucket should slip off the trunk to one side or the other, they can help to keep the tree from springing back and falling
toward you. Similarly, if you want to be sure the tree doesn't fall somewhat to the right, leave the roots on the left side alone.
...but be carefull if it looks rotten, or else you may snap it off where you are pushing from and land half the tree on your cab.
I'll second that. Also, be on the lookout for even a rotten branch high enough, and large enough to do damage. Even though you may be pushing the entire tree away from you, the rotten branch can snap off and fall back toward you. Don't ask me how I know...
Start by pushing gently, perhaps even rocking the tree back and forth a little. That way you get a feel for how easily it's going to go over, and it may need to be loosened up a bit anyway. Only when you get it leaning so that you know it has no choice but to fall where you want it to, should you push with everything you've got. In other words, keep your options open--don't you commit to pushing it over until you know it's commited to falling.
What if you can't burn the trees. Don't think you can burn in this area--gotta load it out to the landfill.
Plan on taking the whole tree down and then dealing with the branches. Their weight helps bring the tree down, and they're a whole lot easier to control when they're laying on the ground in front of you, rather than hanging over your head.
Push with your teeth and use the boom down preassure to push it over, or you can simply walk towards the tree using track power. Reason i push with the teeth is you then have some control of which direction the tree starts falling as the teeth bite into the trunk.
I'll agree with Tyler, with some qualification--be careful that as you apply down pressure with the boom, that the teeth don't dig so far into the tree that it begins to lift the machine. Better you should back off and take another shot than to lift the tracks off the ground and get cockeyed. I'll generally start pushing with the underside of the cutting edge. That way you only have to roll the bucket out a little to bring the teeth into play, and roll the bucket back in a little to keep the teeth from biting into the wood too much.
You've got to be real careful throughout the operation. There's a lot of "spring" in trees and their branches. (Think of the old hunter's snares, made by bending a tree down and atteching a loop of rope to it.) Any time you push on any part of a tree, it has the potential to come springing back at you. Guys have been killed by this.