I'm a web developer professionally and work closely with UI/UX (user interaction/experience) designers closely. There are a few key areas for any seller's website, let alone an author. One caveat is that some of these are guidelines based around the design, so aren't 100% set in stone.
- A call to action should be as easily accessible as possible. For an author, this is most likely an email signup form or social media buttons, or both. You don't want to hide these at the bottom or only on certain pages - you want to have them around the middle of the homepage and clearly visible, and anywhere else you'd catch people - blog posts, contact page etc.
- Offer your product straight away. For an author, you'll want to show some cover work, an extract, a review, basically something to highlight what you're selling. If you make it all about you without your work, you'd be surprised how quickly people turn away without even scrolling down. We find about a third of people don't even scroll down. Maybe they came to the site by accident, maybe they didn't like what they saw, but try and keep them engaged asap.
- Performance. This one is a little more technical but applies to any site. If your site takes a few seconds to load on desktop computers, you're going to lose a lot of visitors. If people are using phones and 4G in a tricky area or even 3G for whatever reason, this load time is significantly increased. People won't stare at a blank screen for more than a few seconds nowadays. Everyone's in a rush.
- Design. This one is subjective, and based on a lot of author websites I've seen, the design doesn't tend to be the highest requirement. However, I'm not solely talking about rich imagery and pretty colours, I'm talking about the layout and structure. If your user is confused about where things are, where to find links to your book, and where in general to look for what they're searching for, then you could lose a buyer. Think simple.
- Target audience. Appealing to older readers? Consider displaying engaging content and blog posts straight away. Young adult? Consider a nice modern design with rich imagery. Children? Something interactive. You get the drill.
I could go on, but I think it's more valuable to show some examples as you've asked for. Some great websites I like:
I like Andy Weir's website:
Andy Weir
It shows everything I want - latest book, clear visual newsletter form, clear links to other pages/media, and also sets a clear design for what to expect from him - space books!
For something with a bit of a more interactive feel but following the same principles above, I like the James S A Corey site:
Home - James S.A. Corey
Finally, I of course like my own promotional website, which at the moment goes against half of what I've said above!