There was a time when 'self-publishing' was an accurate term for publishing a book yourself rather than going through a publisher. In those halcyon, pre-Amazon days, it was easy. At least, I found it so.
A cover from one of my early self-published books
All I had to do once I'd written a book was create a cover using something like Microsoft's WordArt in Word, and some clip art, save the whole shebang as a pdf, and then sell it.
Now, I realise that I may have skipped over a couple of important bits there, so let me elaborate. The cover was easy to do because as far as I know, nobody in those days worried about covers. At least, not in the world of self-publishing, and certainly not in a niche area like educational computing. People were interested in functionality: will this book tell me what I want to know? And the reason I described the pre-Amazon era as 'halcyon' was because when you look on the Amazon website there are so many great covers that the really awful ones stand like like a sore thumb. So artistically-challenged people like myself are forced to think about covers whether we like it or not.
As far as selling it was concerned, all I did was register for an online payment service to handle the transactions. It was possible to install your own payment system on your own website, but frankly who needs that kind of hassle? Marketing, such as it was, took the form of writing about it on my website.
But consumer expectations, greater acceptance of of self-publishing and changes in technology have meant that although you can still do everything yourself, it's more likely that you will need to build a team of people to do different things for you. By 'build a team', I don't mean that you need to take people on as permanent staff members, but hire them for a particular project.
In particular, you will probably need to acquire one or more of the following: editor, cover designer, text formatter, marketer.
In this brave new world, the term 'indie' (independent) publisher is far more accurate. You are independent in the sense that you are not contracted to a publishing company. But book publishing still requires all the services that a traditional publisher provides (or should provide). Unless you can not only write but also format your book, design a cover and market it effectively, you won't be able to do it all yourself.
However, even if you are multi-talented, you have to ask yourself the question posed in Discoverability (Amazon affiliate link), by Kristine Kathryn Rusch: Would I be better off writing (WIBBOW)?
Take formatting, for instance. I recently published my first Kindle book, and the formatting took ages. Even after I'd checked the book in two different programs as well as my Kindle, someone contacted me to tell me there was some strange formatting in one section. So then I had to spend another set of ages dealing with that. Since then I've bought myself a template. If that doesn't do the job, I've decided to just outsource the task: it's a much better use of my time to be writing than formatting if the latter is going to take a substantial amount of time.
So, not self-publishing but indie publishing. It's a much more accurate description of what we do.