Roughly speaking, you can divide 'sharpening' into three categories - grinding to repair chipped or damaged edges, honing to put a sharp edge on the tool, and polishing/stropping to refine that edge for finer work.
Grinding can be with an offhand power grinder, wetstone grinder, belt sander, hand-crank grinder or by coarse abrasive stone (slow, but you don't need a power tool).
Honing can be done one of five ways - oilstones, waterstones, diamond stones, ceramic stones or abrasive papers and lapping films stuck to something suitably shaped (flat, usually).
Polishing can be with a very fine grit oilstone, waterstone, or diamond stone, ultra-fine ceramic stone or by stropping - a very fine abrasive applied to a 'strop' of leather, wood or whatever.
A 'general' approach would be a grinder of some sort, a medium honing stone of whatever sort takes your fancy, and an ultra-fine honing stone and/or strop to put a polished, ultra-fine edge on when it's required. Most people also eventually aquire a small selection of slipstones or pieces of shaped wood with abrasive papers stuck on them to deal with such things as gouges, carving chisels, wooden-type spokeshave irons, moulding plane irons and such which.
It's also worth noting that sharpening is a very personal thing. Some people take to one method, but can't get on with another. Read up as much as you can, take a good look at Youtube videos of the various methods, pick one that appeals to you and stick with it while you get used to it. There are quite a few people with strong opinions about how to sharpen - their method works for them, but it may not necessarily be the one that works for you. I'm afraid that in the end, you have to find your own 'right' way - there isn't one single 'right' or 'wrong' way of going about sharpening edge tools.