When an author is traditionally published, she gets some say in a cover but not much. A lot depends on the publishing house. I was always asked what my initial concept was, and after that they'd say, "Here's what we did." I've had author friends who hated their covers but couldn't do anything about it. I had one I didn't much care for, but I trusted the publisher to do what worked for the masses, not just for me.
As an independent, an author is responsible for everything, including the cover. Knowing I have the artistic talent of a Brahma bull, I hire people to do my covers. I've been lucky to find cover artists who can take my germ of an idea and make it beautiful.
When the first Sleuth Sisters came along, I had no idea it would be a series (or so popular: Thank you all!) I wanted three pairs of shoes, each representing the personality of a sister. Obviously that meant heels for Retta, casuals for Faye, and businesslike for Barb. I hired Clarissa Yeo of Yeocla Designs, and this is what she came up with.
Other things come into consideration too. Lettering is small on Amazon's little thumbnail sketches, so I want to make sure the title and author name are readable. Simple backgrounds are more attractive than messy ones. And color catches the eye as readers page through screens of twenty books at a time.
It's a relief when the cover is finished and I'm happy with it. I could never do one myself--Well, I could but it wouldn't be pretty. I'm perfectly willing to pay for the talents of some artist who says, "Oh, so the book is about three sisters... Let me see what I can do."