A big part of gaining that experience is by pushing yourself into new experiences. Yes, gather as much info as you can beforehand. But when you get in that slightly bigger, slightly deader tree you need to be able to open your concentration to the job at hand and feel the tree. Trust your gut in combination with that you have learned. Study every small variation in the tree. Look at the wood grain after making a cut, remembering how that particular piece reacted when you cut it. LEARN from the tree.
Remember, fear is bred from ignorance. If you are scared it is because you do not understand something. Study the cracks, figure out how it broke and why. Study the areas that didn't break and figure out why. All this will help overcome the fear of the unknown. If you understand the wood, then you cannot fear it. You will become more confident in knowing what will hold and what will break.
I love when I get to remove a new type of tree. I get to compare it to what I already know from previous experience and I also get to observe my own personal theories put into action. I will predict how the wood will react and then study it as I make the cut. When I'm wrong, I try to figure out why I was wrong.
Sorry for babbling. I just really enjoy my work and don't get enough opportunities to share the learning experiences.