Agree with all the previous suggestions, particularly on safety. And a properly anchored block and tackle pulley system is awesome. But you can take down even really large trees with a full size backhoe, if you go at it right.
I have taken out fence lines with many trees in them by first looking at how the tree is anchored by its root system - some almost have a taproot, but many, like wild cherry, have large root "leaders" you can identify at its base. That's your target. I have an old, worn out, Case 580C here on the farm and by making four (sometimes less) re-positions and cutting the leaders out 5-8 feet from the base, you can do this. Once the tree is weakened in this manner, use the dipper/stick higher on the tree to push it over. As it begins to move, you may see other roots you might have to attend to, though, to get it to go.
I will admit after years of doing this, I don't cut the tree first. Not as safe, admittedly - first, you need to pay attention to which way the tree wants to go and an old 580C weighs 15-17K (that's your friend). In any case, leave a long enough trunk to use as a lever for the backhoe's stick. And never get in a position to allow the tree to act as a compressed spring acting in the direction of the backhoe. Take it slow.
I would never attempt this with a tractor type backhoe or a lighter backhoe. And spring rains are your friend in these projects. If you don't feel comfortable with a full size backhoe, though, take it slow, try smaller trees, and be safe. Cutting root leaders will work with the stumps, too and the bucket breakout force can be used to uproot the stump even at ground level.
If you want some new skills, why not rent a backhoe and ask them for the name of an experienced operator? Well worth the price of a few hours instruction to learn backhoe basics. You'll use these skills more than you would think.
Be safe, above all...