How do I fix wiper arms on a 2012 Kia Sedona?

the wiper arms are usually attached with a nut over a tapered shaft. the shaft is tapered and not splined for just the thing you described. if the blades are frozen the motor will burn up, so the tapered shaft turns without trying to force the wiper. try tightening the nut on the wiper arm.

It could also be your wiper linkage is broken since it seems you can still hear the wiper motor working. Here is a link with a break down of all the wiper related parts for your Sedona. http://www.kiapartsoverstock.com/showAssembly.aspx?ukey_product=7208255&ukey_assembly=1068425