Over the years, I've tried several methods of sharpening. The common factor between them was that they all worked. They all had advantages and disadvantages, too, so the 'right' way for me might well not be for someone else.
I started with an oilstone - the ubiquitous Norton India 8" x 2" combination stone. I used it with 3-in-1 oil and an Eclipse honing guide. I didn't get on with the guide (some people do, some don't), and ditched it fairly quickly. One downside of the man-made oilstones is that they're porous, so they absorb oil. They then leak it again in storage, contaminating whatever they're sat on.
Water stones were very fashionable in the woodworking press around that time, so I thought I'd give them a go. King brand stones, a middling grit one and a 6000 grit 'Gold' stone. This taught me what a truly sharp edge was, and how much easier a lot of woodworking is when tool edges have them! It was truly a revelation. Sadly, however, water stones need water, and quite a lot of it - if you can set up a separate sharpening bench with a source of water (sink, bucket, whatever) and means of keeping things managed, water stones are fast-cutting and give good edges, but if you have to sharpen on the workbench, as I did, they are just too messy! Some waterstones are quite soft and wear quickly, needing regular flattening. That's easy if you're set up for it, but again, at the bench, it's a messy job.
So I tried Spyderco ceramic stones, instead; a medium and an ultra-fine. Expensive in first cost, and a bit slower cutting than the oilstones and water stones, but they gave excellent edges. The manufacturers say you can use then dry, but I found they worked best with a few drops of water having a bit of Fairy liquid to kill the surface tension, otherwise they tended to clog and glaze; you can clean then with a pan-scrub in the kitchen sink, but used lubricated the problem is pretty much eliminated. They come in plastic holders, which catch the drips off the sides nicely, so they're much more bench friendly. They don't need much storage space, either.
More recently, I've gone back to the India combination (now kept in a thick plastic bag!) supplemented with an Inigo Jones slate hone, both of which I use with mineral oil, and the slate is used rather like a strop - only draw edges back, not cutting on the push stroke. It's simple, bench friendly, and I don't have water near my tools. The Inigo Jones gives me even better edges than than the watersones did, though it's slow cutting - it's just for the final polish of an edge, not for 'metal shifting'.
All this is done freehand. There's a (long, bitter, rumbling) debate about whether it's better to use a honing guide for repeatable and predictable results, of freehand for speed and versatility. The answer is that only you can decide. The guides give a degree of certainty for the beginner, but add an extra cost and a bit of time to the sharpening task, freehand is quick but takes a bit of practice to achieve good results every time. There's no 'right' answer - though some will insist that their way is 'right' and anyone disagreeing is 'wrong', and post comments to that effect repeatedly and at length - hence the 'popcorn' comment early in the thread. (Quite a few of the forum regulars regard sharpening threads as very dangerous places to go, these days, sadly, because of the attitudes of a few sharpening zealots.)
I haven't tried diamond stones or 'scary sharp' lapping films, but both methods work, and work well, and have their own devotees. Don't dismiss them - though they too will have their own pros and cons.
Two other things I haven't mentioned so far are grinding and stropping. Sooner or later, you'll need to consider grinding, and that's a bit of a minefield too. I think I've rattled on long enough, though.
There's plenty of information on sharpening out there (books, blogs, YouTube), probably more than enough to confuse the beginner and frighten them witless. Don't be disheartened by it - sharpening is basically a fairly simple process, though like just about everything else in life, it does take a bit of practice to become confident. It's worth the patience and practice, because once you can keep sharp edges, woodworking becomes much easier!
Good luck!