The wood lathe is my favourite woodworking tool - hands down. Follow this link to me simply having fun.
The most important safety detail in woodturning, after a face mask, is to learn to properly place, and constantly adjust, the chisel support. It should always be close to the wood to leave you in control but just far enough back to allow you to use the support as a true leverage point. By the way, if you have white knuckles while turning wood, you have not learned how to use the chisel support yet.
Most people learn wood lathe work as a scraping job, as you see in the first photo. To scrape properly you must place the support quite high so that the chisel can point downward into the heart of the wood and the lip of the scraper will literally scrape off wood. This is the safest, surest and least scary way to produce wood turnings. It is also the slowest, most boring and requires the most sandpaper to repair all the damage. Some very light scraping is sometimes appropriate but then it is even best to burnish a burr on the end of the scraper so that despite the negative angle, the little burr is actually slicing wood.
If you want to enjoy wood turning, you must learn to cut or slice with a chisel. For this the chisel rest is placed much lower. The objective is to rest the heel of the chisel on the spinning wood and then pull the handle back, still resting on the support. This will lower the angle as you pull the handle back, until you feel the cutting edge engage in the wood. The heel of the chisel and the support is what gives you control. If it starts to grab too much, move the handle forward (a counter intuitive thing to do), the chisel will ride up on the curve of the wood and disengage the cutting edge. You play back and fourth with that cutting edge with almost all the control in your rear hand. The longer the chisel handle, the easier this is to control.
If you are really not sure about slicing cuts, start out with the chisel on the rest and literally sticking out above the wood. Pull back slowly until it barely engages, then play left to right and back -- bite more -- bite less. After that you will want to turn the chisel on its side a bit and slide down hill into the curves of the spindle, rotating the chisel as you go to a flat position and pushing the handle forward. That twisting sliding forward swing the arm to the side action will eventually become natural as you deepen the curves.
Most beginners are afraid to try rounding off a rough square piece with a chisel. The key is to have a large chisel with a long handle and a perfectly square face that has a deep curve and is sharpened as a chisel. This roughing out gouge gives you the control you need when half the time the chisel is not even touching the wood. As you take the square corners off, rather than stopping the lathe all the time to know if you have gotten down to a round surface, simply rest the chisel itself in the groove as in the next to the last photo above. It will bounce and clatter if there are still flat spots. When it hums, you have finished your roughing out job and can begin slicing shapes.
Of all the many lathe books I have to recommend a very old one to you, that you may have to seek out as a used book at Amazon.com, not because Peter Child is the best craftsman on a lathe, but because he is the best I have found for teaching through a book: The Craftsman Woodturner by Peter Child, published by G. Bell & Sons Ltd. London 1976.