From the sounds of it, this is a relatively easy fix.
If the existing clamp on the hose is in bad condition.....
Go to home depot and buy a clamp just large enough to fit your hose. Should be about 1/2"
Undo the clamp on the radiator where the leaky hose is. Gently pull off the hose, it may take some effort. If there's any crud left on the radiator nipple, clean it off. Also this is pretty much a given, but just make sure not to get any dirt or crud into the hose.
Cut off the worn portion of the hose, should be No more than an inch.
Put ONE DROP of transmission fluid on your finger and smear it along the radiator nipple (wutang!.... not a word!) so that you have a little lubrication and your hose fits smoothly.
Finally thread the clamp onto the hose, Gently attach the hose to the radiator, and screw down the clamp. Don't over-tighten and you should be all set.