My cameras battery area is corroded! how can I replace this?

Keeping the camera upright so nothing drips inside of it, a mixture of water and baking soda will clean things up. Apply with multiple foam Q-tips to get up inside the battery compartment. Use high-strength (91% or higher) isopropyl alcohol on a foam Q-tip to clean out the baking soda mixture.

@snap2 as this is corrosion caused by the alkalinity of the battery I always use a water/vinegar mix and a cotton tip applicator to apply it. Use a toothbrush for larger, more corroded areas, like the battery compartment cover etc. In your case, I suggest that you actually dismantle the camera for a good cleaning. That way you can be assured not to get anything into the camera, which could cause other problems.

Generally to clean up corosial I use a bristle brush or qtips dipped in the highest concentration isopropyl alcohol I can find. Once done with that I would leave the camera to sit for a few hours to make sure any remaining liquid dries up and evaporates.