There are a few things to consider.
Kindle (Amazon) is easy enough. You set up an account, fill in the tax info (there's even a YouTube video to guide you through the steps), upload the book and it'll be online for sale within a few hours.
You can set up paperbacks through them, too.
You can put your book in Kindle Unlimited (so it's available for KU subscribers with their subscription) or you can 'go wide', in which case you'll be looking at also uploading to the likes of Kobo, Apple, maybe Draft2Digital and Smashwords, etc. They all have their own storefronts and tax info to sort out.
For hardbacks I believe you'd have to go through someone like IngramSparks and buy your own ISBNs. Canadians and Australians get theirs for free, I believe. In the UK (like the US) we have to pay, unfortunately.
If you're only selling via the likes of Amazon and Kobo and other storefronts, they'll take care of the VAT side of things, and you'll just have to report your income from your books via self assessment (and register with HMRC as self-employed). If you want to sell directly via your website, you'll have to collect VAT and pass it on to HMRC.
There are also book covers (including a wrap-around cover for paperbacks), blurbs and other marketing things to consider.