There are many ways you can do an e-book giveaway, but the most popular is through websites such as BookBub (the leader of the pack by a mile), Freebooksy, The Fussy Librarian, Robin Reads and way too many more to name. As much as you might not like signing up for Amazon KDP Select (this allows you to give your book away for 5 days each 90 days on Amazon with the caveat being it has to be exclusively available on Amazon), it is a necessary evil if you want to gain any traction. Bookbub is the holy grail for most authors but as well as being the most expensive, it is also the most difficult to get accepted by. I chose Freebooksy as they were not too expensive and had dates available within the next week. They also have have a large following.
Following the free day I did have a big increase in full price sales - although this did decline after a few days. Still, it was great and amounted to more sales than I'd had the previous few months combined. So that was a definite plus. The main way I've increased income has been in pages read in KDP Select and Kindle Unlimited. Three months on, this is holding steady in the thousands per month as people get around to reading my book on their Kindle. Although the income from this is not huge, it is still income and will add up over time. I have also had some increase in sales for my other books at full price. Most importantly I have also gained 11 new reviews on Amazon.com, which is a huge bonus.
As much as we might not like all the things Amazon does they are the biggest book retailer on the planet and their tentacles reach far and wide. Making my book free for one day put it in front of thousands of readers who otherwise would never have seen it, let alone read it. So in that way giving away free copies is not lost revenue, because most of the people who downloaded it would not have purchased it anyway. As a reader I have downloaded free books and gone on to purchase the author's other books, so I know it is possible to gain new readers this way.
Another sales strategy is to do a 0.99 cent promotion. It seems like a better option on paper. After all even though you will only get 0.34 per book sold, that will add up when you make hundreds if not thousands of sales, right? Well, theoretically yes. However the reality is that most readers are less willing to take a punt on an unknown author when they have to pay for the book, even if it is a measly 99 cents. Comparing the two strategies, with a 99 cent promo I didn't even make three figures whereas the free promo hit the thousands. As an author it is annoying that one dollar is too much for some readers to spend, however it is what it is and being annoyed and thus not trying a free giveaway will not gain you that longed for exposure.
Ultimately each author has to decide for themselves whether they want to try out the book giveaway strategy. Yes it does seem counter intuitive, but if the end results is strong and ongoing sales for your book(s), then I believe it is worth it.