Self-publication is the act of independently publishing a book, generally using an Internet provider, such as Amazon's Kindle Direct Publishing (KDP). (Other self-publishing platforms are available!) A user account is required; although, where a client has an existing Amazon account, this can be used to access KDP. Two files are normally required in order to self-publish a printed book: the author's typeset (and proofread) manuscript, and the book cover. These two documents are uploaded to the provider's platform. Once publication is approved, the book is advertised on the site's retail page. The author can generally order discounted copies of their book. Each time a book is sold to a customer, the author receives a small sum of money known as a royalty.
How I work: In the absence of client preference, I use Kindle Direct Publishing. I am familiar with its operation, and their service is currently free; however, I am happy to work with clients who wish to use other self-publishing providers. Although the client must set up their own user account and manage it, I do offer help and support with this. I recommend that the client signs up for their user account at the outset of the project, so they are familiar with the setup process by the time their book is ready to publish. Simplified, the general order of events, when using KDP, is to add paperback details; upload paperback content; and set paperback rights & pricing. (A separate similar procedure is used for an e-book). The ISBN is relevant here.
How long will it take? Once the final copy of the typeset document and book cover has been uploaded, and approved by KDP, publishing can take up to 72 hours before the book appears on the website and is available for customers to buy.
How much will it cost? It is currently free to set up an account on KDP and use their self-publishing tools, and I do not charge to assist with this. However, there will be external charges to the client if a UK ISBN is used. As at January 2020, a single ISBN will cost £89.00. 10 cost £164.00. You need a different ISBN for each type of published media: paperback and e-book (so that's two for a start.) ISBNs are supplied from Nielsen Book, who run the ISBN Agency for the UK and Ireland.
What happens next? We congratulate ourselves on a job well done! However, for you, the author, there is some post-publication business to deal with: perhaps some further marketing of your novel. See the page Beyond publication.