Yes, we have SOME bananas! We have SOME bananas today!
In fact, because of the recent series of mild winters we've had, more and more people have been calling about actual production on their banana trees. (Although they aren't truly a "tree" because there's no bark. But that's a tip for another day.)
Everyone wants to know how to make sure their bananas get bigger and ripen so a real crop can be harvested. This is an admirable goal, because once you've tasted home-grown bananas, you'll never want those from the store again. (Sort of like tomatoes.)
If you're lucky enough to have a bunch of bananas hanging from your tree, here's how to take care of them. Once the fruit has stopped forming, and the bloom petals have dropped from the maroon bulb hanging below the bananas, cut off the bulb ... but only if you have something of a stalk between the bulb and the bananas. In fact, you should cut the stalk leaving 10-12 inches below the forming bananas. Theoretically it will continue to grow, but cutting will prevent the stalk from rotting. The bananas will then attempt to round out on the tree. This can take two to three months in some cases, so patience is a virtue.
Once the bananas have rounded, you can assume they are as big as they're going to get. That's when you cut the entire stalk off the tree and store it in a semi-warm but dry place. You can speed up the ripening process with ethylene gas either by placing apples near the ripening bananas, or by placing the bananas in a perforated plastic bag ... one from a dry cleaner and punched with holes is good.
For more on growing bananas, check out this webpage.