Corrosion on the terminals is due to hydrogen gas being released from the acid in the battery. It mixes with other things in the atmosphere under the hood and produces the corrosion you see on the terminals. Generally, if the corrosion is occurring on the negative terminal, your system is probably undercharging. If on the positive side, it is probably overcharging. Most often it will be seen on the negative side because the battery is usually in an undercharged situation. This is just the nature of the beast, I'm afraid.
You will need to thoroughly clean the corrosion from off the posts. You can use baking soda and water solution to help in this endeavor. Ensure you have eye protection, clothes which you don't care if it possibly gets ruined (acid can do nasty things), and some type of gloves (nitrile gloves work great). Clean the area using the solution and a brush. It doesn't have to be a steel bristle one, just one which is stiff enough to remove the gunk. You will have to remove the battery cables to get them completely clean (sorry about the radio channel presets!). Finish your clean up with a good dose of water to flush the area of any residual corrosion. If you don't, it can eat away the paint in the nearby areas.
When done cleaning, to help slow down the corrosion process, coat the terminals with grease (high pressure grease or wheel bearing grease works as good as anything). It doesn't have to be a lot, but ensure total coverage of the metal at the terminals. Cover the outside of the terminals after you have put the cables back onto your battery. You can also purchase a aerosol spray coating which you can purchase from your local parts store. Your main objective is to keep the lead, escaped hydrogen gas, and oxygen from mixing which forms the corrosion you see after a period of time. Over time the grease will break down and corrosion may start, so regular cleaning and reapplication is a must. If you do this about every six months, you should be in good shape.