I have a Canon Power Shot A470. I have replaced the batteries many times, always with brand new ones, and it still keeps telling me to change the batteries. What is the problem with it? How do I fix it?

Yes, but what batteries have you been changing? If the AA's, those aren't the clock battery. Open the battery door, and notice the tiny door inside labeled "CR1220". Pry that door open with your fingernail, and take the enclosed CR1220 battery down to your local drugstore to purchase a replacement clock battery. Drugstores seem to be cheaper for this battery (~$3) than retail outlets like W-Mart (~$7).