The best way to start DIYing your own furniture is to pick a beginner project and dive in, and learn as you go. Make sure you pick a good plan that requires minimal tools, with a video tutorial, detailed diagrams, shopping and cut list to help you along the way.
DIY furniture is a skill that requires hands on learning experience. You can read about using tools, but there is no substitute for doing.
Start with a small, starter project with minimal materials. Use pine wood or whitewood boards, as the wood is cheap and easy to cut and work with. Buy a little extra material to practice cuts and joinery.
Think long term, it will take a few projects to develop the skills to whip out furniture quickly and easily. Use this time to experiment with different joints and finishing techniques.
There are many different ways to build your own furniture, but most DIYers end up with the same set of tools and techniques: a drill, miter saw, pocket hole jig, brad nailer, circular saw and power sander.