I know three people who have self published, and all have done it on Amazon/Kindle as they found the cost to be manageable. In all threee cases, the publicity was done on social media to friends and acquaintances, and it picked up from there (in one case the author had some 3000 contacts on Linked In and he sold 6000 copies/downloads). Worth noting that in all three cases, they weren't expecting to retire on the proceeds, it was done for a bit of fun.
If the author is really intending to make a go of this, I'm not sure self-publishing is the way to go, unless you have the media machine to go with it. You need access to blogs, reviewers, press (printed ads in the Tube and around bus stops is apparently very much worthwhile), media serialisation, etc. etc. To do that off your own back represents a heck of a lot of cash.