After preparing the post in fastest riders on earth, there was a guy who can ride backwards really fast, what does it take to ride backwards at all? Let's see.
First things first, the trick riding that fixed gear riders do is not actually the "official" way to ride backwards.
How it's actually done is when you sit on the handlebars and steer with your hands backwards, pedaling on any bike (fixed gear or not). And it is called reverse cycling!
Anyway, a lot of fixed gear riders can reverse cycle as well, it's one of the most common practices you learn in order to do tricks on your cycle. You stand in a trackstand and start pedaling backwards, it's easier to start in circles and then going in a straight line after rolling backwards from a small elevation.
In some time maybe you will be skilled enough to do a wheelie!
There is another way to cycle backwards not literally, but with a special bike, that makes your brain not understand how a bike operates if a steering function is changed, amazing video, watch it!
You can actually purchase this bike and try it for yourself, see the video description!