This introduction to self-publishing originated as an email to a friend wanting to step into the self-pub ocean. But I think other people might enjoy it, too!
So: Self-publishing is hard, in that it involves a lot of tiny details to manage, and all of those details actually matter. But it's not hard in that you don't need to be a rocket scientist to work your way through it, just... a lot of diligence.
Let's assume you've already written what you want to publish, so your first step is quality control -- getting the material edited. If you're reasonably literate you might be able to skip this step, but it's always best practice to get another set of eyes on the material. I've been a professional editor and I still hire someone else to read behind me, because you can't always see your own mistakes.
Then you need a cover. Cover art is your #1 most important marketing tool, so you're going to need something that looks great, has a feeling in keeping with the genre of book you're putting out there, and is legible and eye-catching even at thumbnail size. Here's some cover design advice ...but unless you are yourself a designer already, you're best off shelling out some money to someone else to make one for you. Find one through your friends or through a service like Bibliocrunch.
Next comes figuring out how to get that into an ebook format. All you need these days is an .epub file. Kindle sells .mobi, but you upload to them as .epub. Apple have their own proprietary format, but if you work with an aggregator like Smashwords or Draft2Digital, you provide them with an epub and they'll do the conversion. Epub is all you need.
There are a bunch of ways to convert. Pay attention to formatting paragraphs and chapter headings the way you want them to look, but less formatting is better than more. You CAN insert art as custom scene breaks and so on, but images make the file size bigger, and Amazon in particular sometimes charges you bandwidth fees for image-heavy books. Including art or photography inside your book is advanced stuff and not recommended.
Remember to put in a cover page, copyright notice, a dedication if you want one, a table of contents, an about-the-author section, and links to anything you'd like to cross promote (website, social media, mailing list, other work).
I like to use Scrivener to export my epubs, because it's easy and mostly foolproof. Instructions on how to do that are here. You can also Google around to find instructions for MS Word and so on. But Scrivener is rad and you should give it a try anyway.
Next, you choose where you want to publish and your pricing strategy. You have to be on KDP, which is Kindle Direct Publishing, which is Amazon. The lion's share of self-publishing sales come from there. There are other stores, too, most notably B&N, Kobo, iBooks, Google Play. There are also a few genre-specific publishers, though the only ones I'm aware of are for romance and erotica.
If you want, you can open an account and publish to each of these stores directly, but that becomes a huge pain in the neck to manage. You can also use an aggregator like Smashwords or Draft2Digital and manage everything from one account. Smashwords has very onerous formatting requirements for their books and I've never been able to figure them out, so I use Draft2Digital and have been very happy with the service. Note that an aggregator takes a small percentage of your royalties, above and beyond what the store takes as their share. Decide if it's worth your time to make those extra couple of cents per sale by setting up multiple distribution accounts. Lots of people split the difference by having an account on Amazon for KDP only and then an aggregator elsewhere.
It's ALSO a good idea to provide a venue for readers to buy from you directly. There are a number of services that let you do this, like Gumroad and Payhip. The benefit here is you keep a much higher proportion of the money that you would through any store. Some writers I know actually do the bulk of their sales direct-to-reader in this way.
You should also know about KDP Select. This is a program Amazon runs for publishers who promise them exclusivity. In return, you get the ability to run a couple of kinds of promotions -- like putting your book up for free or at a discount for a few days each quarter. This used to be GREAT for producing a sales spike but isn't really worth it anymore; Amazon has changed its ranking algorithm, so free book offers tend to result in less-flattering reviews and no additional sales. And the opportunity cost for the sales you're not making through other channels is too high.
On the other hand, there's Kindle Lending. This is something you can opt into or out of. It's a very, very good idea; the royalty you get from a borrowed copy is historically much higher than the royalty you get from a direct sale, so it's a win all around. Opt into that like whoa.
On to pricing strategy! Many of the ebook stores require you to give them the lowest available price, so it's best practice to just use the same price everywhere. But what should that price be? Note that Amazon gives you a 70% royalty on books above $2.99, but only a 30% royalty for lower price points. So $2.99 for a full-length book is probably your basement. On the other hand, $7.99 should probably be your ceiling; I'd probably price a full-length book at $5.99 to split the difference. (On the other hand, novellas and short stories can do booming business at .99 and 1.99).
Cheaper is not necessarily better for sales, believe it or not! Readers have become very cautious of poor-quality, cheap ebooks. Be confident in your pricing strategy!
Once you send everything up live, be sure to get your friends and family to leave reviews for your work! The biggest obstacle to sales is obscurity, and the more reviews and sales a book has, the more visible it's going to be on Amazon.
There are other issues you need to also be aware of, or at least look into: marketing and promotion, making and selling physical books, and if you're lucky enough to sell well, self-employment taxes. But each of these is an enormous topic in its own right, annnnnnd I think that's about enough for one day. Good luck to you, and many happy sales to come!