Backyard Leveling & planting beds

Welcome. A lot of it depends on what you're starting with. Tilling of course loosens things up, and makes it easier to rake in low spots or rake down high spots, so it's a good way to approach bare soil. But, if the lawn is otherwise in decent shape, mostly healthy grass, tilling it is going to produce a lot of clods that are going to make it more difficult to deal with. In this case, you may be better off bring in dirt to fill the low spots and then seed those areas. I have heard of some who would kill whatever is there with Roundup or whatever, then till it, but you still have the roots that are going to bunch up, plus it turns it into a lot longer process by the time you wait for everything to die. Around the trees, if you're going to have grass up to them, I would approach the same as the rest of it, till if warranted, otherwise fill the low spots. If you're planning a mulch bed around them, then I would probably till it, primarily to loosen the soil to make it easier for the water to soak down around the roots, rake it out as much as you can, and spread your mulch. Just one persons approach anyway.