One of the main differences between shotshell loading and metalic cartridge is the limitations on load recipes. You must use a published, tested shotshell load to be safe. You can't just swap components as you could with metalic cartridges. For rifle, I could swap a Hornady bullet for a Sierra (of the same weight) without any real impact. You cannot just swap wads in shotgun loads the same way. Not only could there be significant pressure excursions, but the load may not stack up right to fit in the hull and achieve a good, firm crimp. Without a good crimp, your load will not perform ballistically. The shotshell load specifies the hull, the primer, powder, wad, and weight of shot. (Size of the shot is interchangeable, with some limitations. 1 1/8 oz of #9 does not have the same volume as 1 1/8 oz of #2.)
The process of reloading is similiar to what you've done in metallic cartridge reloading, except you need a wad and a load of shot where you had just needed a bullet before. Steps are: size/deprime, reprime, powder charge, load and seat wad, load shot, crimp. The crimp could be two or three separate steps, depending on the machine. Some machines do not size the hull, and many times it is not required. Shotgun pressures are a lot lower than metalics.
For equipment, you'll need to decide if you want a single stage or progressive press. As in metallics, it is price vs. speed, although the progressive shotgun press is a bit cheaper than a progressice metallic reloading press. I like MEC shotgun loaders, and if you opt for a progressive, look to a used MEC 650 or Grabber press.