Making soap can be really, really simple, if you want it to be. All you need as far as ingredients are lye, distilled water (or any number of liquids, including milk, but milk soap is a little trickier to master), and fat.
As far as equipment, you need a dedicated (by which I mean don't use it for anything else) plastic pitcher in which to mix and cool your water/lye solution, a plastic flat-bottom bucket in which to mix the lye-water with the fat or oil, and some kin of mold to pour it into. That's really it! For best mixing, a cheap stick-blender (easily had for less than $10) really helps, though you certainly can stir it by hand until trace, if you have plenty of time and a strong arm.
There are lots of books on soapmaking, and LOTS of websites and supply houses. You can use anything from corn oil to lard to make soap--it can be humble and rustic or gentle and fancy...no matter what your ingredients, it's just saponified fat. There are online "calculators" that allow you to just plug in your ingredients and have the formulas figured for you.