The key to dehydrating bananas successfully is to put them into something to keep them from browning as you cut them. I usually use pineapple juice because I like the touch of sweetness it gives them. You can also use Jello powder to sprinkle on them before dehydrating (think chocolate covered bananas or strawberries and bananas). Note that these banana chips will be different from those that you get at the store. They are chewier, but are very good!
By the way, if you don't have a dehydrator and don't want to spend the money on an Excalibur right now, I recommend keeping an eye out at your local thrift store or at garage sales. You can sometimes find them for just a few dollars. The Excalibur does open up other options (like making yogurt, allowing bread to rise, etc.), but a basic round dehydrator would at least give you and idea if you are going to like to use them to dry foods.