If you've got a book published, whether with a big name publishing house, you've done it yourself on a shoestring, or anything in between you're going to need to promote it. Writers are often told we need to 'build a platform' on social media, so tweeting and making Facebook posts is an obvious thing to do.
Personally I do think it's sensible to mention our books that way – but only now and then. I've seen writers send out multiple tweets per day, sometimes even per hour, all just asking people to buy their book. I can't tell you if they're still doing it, as I've unfollowed or muted them all. It's better, I think, to tweet about the book and your writing life, and include some non promotional stuff too, than do nothing but masses of straightforward promotion on social media. After all, if you want to buy books is that where you look? And when you use social media is it a stream of adverts you're hoping to see? (By the way, here's the twitter profile for this blog and here's my personal one.)
It's possible to pay for social media advertising. I don't do that myself, for the reasons above, plus it's expensive and sounds complicated, but I know they can work well for people who are prepared to put in the time and risk some money. Paid advertising on Amazon is something I've dabbled in. To me that makes more sense as we're targeting people who want to buy books like ours, but might not otherwise find them amongst the millions of others on offer. Again it takes a little time to learn how to use them, and there's a risk of spending money for no result, but you can set daily limits and it's easy to make changes.
Winning a writing competition would be good publicity. My first novel publication came about after I won a novel writing competition. Although that wasn't a massive success and I've since got the rights back to Escape To The Country, it was a big boost to my confidence at the time and in the long run helped me become in Indie author. (I'll be back with more free to enter writing competition links soon.)
Newsletters are an excellent idea, as people will only sign up if they actually want to hear from us and learn about our latest releases, promotions and other news. It's a requirement that people can easily unsubscribe which is good because we know those who remain on the list really want to be. It's common to offer a 'reader magnet' which is usually a freebie, often something exclusive to newsletter subscribers. For my newsletter, I offer a free short story. As a lot of my books are collections of short stories, that seems sensible.
Another thing you can do is have a blog and pepper it with mentions of your own books, along with everything else you post about. You might have noticed I do that! If you don't have your own blog then I don't blame you – they are time consuming. In that case you might like to write guest posts for someone else's blog. You'll need to do a little more than send out blanket emails to every blogger you know asking them to promote you though. Read the blog, and leave comments so you're not approaching as a stranger. Think about the type of post which might interest readers of that blog and offer something appropriate. If you do more than one guest post to different blogs, don't send exactly the same text with exactly the same photos. That's not fair.
A website is another possibility. Here's mine. They do take time to maintain, but are a good way of making it easy for interested readers to find out more about you and your books.
Perhaps you could get interviewed, or otherwise included, on a podcast. I've done a few of those.
Local newspapers are a good place to try. That could be paid for ones, the free ones and online newspapers. The latter are likely to be easiest to get into as they're not restricted for space the way 'real' papers are. Whichever you try, don't just send them a 'buy my book' promotion, but try to make it personal – local papers like pieces about local people. To further increase your chances of it being accepted, make the article as locally relevant as possible. Even if it wasn't set in your home town, maybe you wrote some of it in a local coffee shop, or used the local library for research.
You could try national publications, but unless you're well known and/or pay well you're unlikely to be successful. However if you are one of their writers you might be lucky – it's definitely worth at least mentioning your book to your usual contact. This is what happened when I told 'my' People's Friend editor about my first audiobook.