Approach 1 is to go for tried-and-tested authors: this is great providing they have published Kindle editions, and providing their Kindle editions are any good! Many traditionally published books are scanned in with special reading software and converted into Kindle editions. The problem is - the reading software isn't always that good! In a book I read recently 'Penn Station' had become 'Perm Station' - great for hairdressers but not quite right. The same book was littered with errors, and very irritating to read. The great thing about Kindle, of course, is that you can get a refund for up to seven days after purchase, so this downloaded was quickly returned.
Approach 2 is to try Amazon's recommended titles, or to look at what similar books other readers have downloaded. This can be successful, as Amazon employ a complicated system of looking at your browsing and buying history and matching you p with possible titles. Not that they always get it right, of course, but it's a good way to take the guesswork out of trying something new. Oh, the joy of finding a new author...
Approach 3 is to browse other book websites, such as goodreads.com, and then find the Kindle edition if you can. GoodReads is a fab resource, if a little time-consuming, but worth a look. Many authors (myself included) have Q&As on there, which is a rare chance for fans to connect directly with their favourite authors and ask questions about books they've read. GoodReads also has discussion groups, free giveaways and lots more, so head on over if you need some inspiration.
The one approach that doesn't seem to work so well is to browse Amazon's own listings. The categories are confused and mixed up, and unless you know exactly what you are looking for, it's a pretty soul-destroying task. And their algorithm for sorting books by ranking is incredibly complex, and looks at recency of a book's sales as well as total books sold, so you could easily find a title which has sold very few books but in a short time-period sitting much higher than a book that has sold millions of copies! Still, finding a good book in any setting is difficult - imagine a bookshop with over 3 million books to browse through - so why should Kindle be different? At least a great book is worth the effort.
And don't forget to leave a review for your Kindle title. Authors rely on these to be visible to new readers just like you.