Its real helpful to take an old style click together pole saw in the tree that has a hook on the head. That way you can hang a foot of climbing line on it with a steel biner, drop it through a fork, and pull it back to yourself. With some practice you can handle to 8 ft sticks. With two lines angled apart at least 30 degrees (well overhead!), you can branch walk with ease, and do a lay back and go up or down a side trunk at any angle; on top, to the side, maybe on the bottom.
Remember if you go way out from under your tie ins, you want two lanyards or a third rope so you are always tied in as you move--- the first two cease functioning as a fall protection system at some point. That uncontrolled pendulum swing is not a good thing. A controlled pendulum swing is entirely different.
With two ropes, you can also transfer across a gap you would not want to swing across or which you can't get to by pushing off. You gotta think in three dimensions at all times, and where your tie-ins want to send you from where you are at, and if it would be tolerable to go there if you lose your footing; if not you may not be tied in, but only relying on a positioning lanyard, which, guess what? When you unclip it, you are not tied in with it anymore.
You also have to do more than read posts like this before you do technical stuff. Awareness and skill comes with time and experience. Its also no fun freezing in place and realizing that you could be up there for a good long time because you are "stuck". You also need to stay calm and focused; you can cut your rope or yourself in an instant. I once threw my rope out of a tree (the entire rope) when I was 30 ft. up standing on a limb, because I was untangling it and had untied it. Doh. Had to come down on a flip line alone (no spikes on), and it was too short to use all the way down; I had to downclimb the last bit with my fingernails in the bark. Which brings up one more thing -- don't climb alone.
I share this stuff as cautionary tales. And I still consider myself a careful climber, who has made some mistakes that I am aware of. One thing I am quite focused on and conservative about is the quality of my tie ins -- I often move them to a stronger union or angled differently to help with the next moves. If you can, always put the rope around a vertical stem over several branches, or reset it that way when you climb up to it. Failed tie-ins are a significant factor in bad outcomes -- knock on wood -- not for me, I would like to think because I pay close attention to the tree.