Transformer design can start out simple, but get complex in the details.
But first, some caution: There are two basic approaches to the design, and the experienced engineers treat each of these approaches almost with a religious zeal hurling negative comments at the apostates of the opposite camp. The two approaches are called "core geometry" and "area product". So, as you examine different application notes, and notice that, at first, they seem similar, but strange numbers suddenly appear without source explanation in one application note, and in another application note other numbers appear and are used, you may be encountering the different basic approaches to practical transformer design. Also, if you find that one magnetics vendor publishes one set of characteristics to describe their offerings, but other magnetics vendors publish similar, but different characteristics, you may again be encountering the different information needed for the different design approaches. Without knowing what is behind these numbers, or how they are arrived at, it becomes hard to convert between them, or to take one set of magnetics information and convert it into number useful for the other design approach.
That said, there are several books (five ?) by Colonel Wm. T. McLyman: Magnetic Core Selection for Transformers and Inductors, Transformer and Inductor Design Handbook I consider these books the standard for transformer design, and he gives step-by-step examples of design that are detailed enough that you can construct an Excel spreadsheet as a tool to a particular design. You can find design examples by McLyman by googling. You can also go to coremaster.com and look at their app notes written by McLyman, including toroid transformer design, but the data available is for the somewhat-specialized nanocrystalline cores coremaster offers.
Another website to browse is ridleyengineering.com which covers the whole of power supply design from A to Z.
