Casting on methods are techniques used to create the initial stitches on a knitting needle before starting a project. The most common methods include the Long Tail Cast On, which uses a tail of yarn for a flexible edge, and the Slip Knot Cast On, which is simple and quick for beginners. Other methods, like the Cable Cast On and Knitted Cast On, offer different levels of stretch and appearance. Each method serves a specific purpose, allowing knitters to choose the best option for their project based on the desired edge and fabric characteristics.