Laptop Magazine has an article on this:
The built-in App store on the Kindle Fire offers a decent selection, but it doesn’t have everything. For example, you can’t download Tweetdeck or TripIt, or alternate browsers like Opera Mini or Firefox. While Google’s Android Market is off limits to Kindle Fire owners, you can install apps that aren’t available on Amazon’s store by transferring them via USB (also known as sideloading).
Here’s how to sideload apps on the Kindle Fire.