This answer is generally from a hand tool perspective, but much of it also applies to power tools.
These are some of what I consider to be the basics of woodworking:
1. Understand wood, its structure, and its limitations. This will help you select quality boards, process them, as well as correct many of the defects that a particular piece of wood may have. Keep in mind that wood – unlike plastics and metals – changes dimensions with changes in humidity, not changes in heat; it is a factor that affects your design, joinery, and many other aspects of building a piece of furniture. Learn how to read the grain in the board. This will help you determine the best direction to cut, plane, scrape, etc. Planing against the grain and causing (severe) tear-out is one of the faster ways to ruin a good piece of wood and a project.
2. Perform accurate marking and measuring. If your marking and measuring are inaccurate, then you’re just wasting wood. Accurate marking and measuring requires accurate marking and measuring tools. For furniture building, a tape measure and a cheap hardware store combination square are not going to do what you need them to do. Spend the money on a good quality steel rule and a Starrett combination square; you’ll be glad that you did. Buy an accurate try square, or make your own. Use a marking knife to mark your cut lines; darken the knife line with a .5 mm mechanical pencil, if necessary. A pair of dividers and a knowledge of basic geometry will save you a lot of time in layout tasks and help you avoid trying to measure ridiculous dimensions like 37/64ths of an inch wide dovetail pins.
3. Learn how to cut to a line, whether using a hand saw, a back saw, or a table saw; this includes trimming to a line using a hand plane, spokeshave, or a chisel. This becomes particularly important when you start cutting joinery, such as mortise and tenon or dovetail joints. Accurately cutting to a line saves you much time and effort with trimming and fitting, and results in a better looking piece.
4. Learn how to effectively use a hand plane. A hand plane can help you sneak up on a perfect fit, shape your wood, and will save you lots of time and effort putting a final finish on your surfaces; it also saves you from all of the dust and tedium of sanding through the grits. A hand plane also allows you to dimension wood that won’t fit on your power jointer or through your thickness planer, without having to cut the board into narrower pieces.
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5. Learn how to effectively use a chisel. Not only can chisels be used for chopping, but they are very effective for doing minute precision trimming, flattening the bottoms of grooves, chopping mortises, etc.
6. Learn how to accurately bore a hole. Whether using an egg-beater hand drill, a bit brace, an electric hand drill, or a drill press, you need to learn how to control the tool to put the hole exactly where you need it, at the necessary angle, to the proper depth, etc.
7. Learn how to sharpen. If you are going to use hand tools, you must know how to sharpen them. Otherwise, you’ll be endlessly waiting for your sharpening service to get them back to you. Besides, dull tools are dangerous, don’t work properly, leave a poor quality surface, and are a trip to the emergency room waiting for a time and place to happen.
8. Understand finishing: what the various finishes are, their strengths and weaknesses, their appropriateness for different uses, safety, stylistic effects, period appropriateness, application techniques, troubleshooting, etc.
9. Learn how to build and use the various appliances – shooting boards, bench hooks, bench jacks, sawing benches, etc. – to make your work more accurate and more efficient.
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