Self-published authors have a number of options available to them. They can publish their books directly through online retailers like Amazon, Sony Kobo, Barnes & Noble, and iTunes. They can also go through redistributors such as Smashwords and Draft2Digital, which are companies that will create differetn formats for your book and then distribute those formats to each of those same online retailers and others. The royalty that an author gets will vary depending on whether they publish directly or go through a redistributor, and it will also vary based on price, but generally it is between 60-70%. As a self-published author myself, I'm perfectly content with any format as long as someone is buying my books!
Authors who are published through one of the major publishing houses like Putnam or Harlequin will often receive a much smaller royalty which is agreed to in a contract up front. This can range from 6% for a new author to as much as 20% for a developed author. Alternatively, these authors usually also receive a guaranteed advance on their sales, so even if the book is a bust, they will have something to show for it. In spite of this, more and more authors are beginning to reclaim the rights to their back titles and sef-publish them because they have better potential there.
If you truly want to help an author, the best thing you can do is leave a review on whatever site you purchased the book from. Often times the reader reviews are used to help with the recommendation algorithms, so when other readers who have expressed an interest in similar titles visit the site, that author has a better chance of being recommended by the site's built in tools. Telling others about the book will also often help in generating additional sales, and those are always welcome!