Need to unscrew the little hand grip thing on the left hand side (as you look from the front). The battery compartment should then be obviously exposed. Put the 6V battery in, like one Rob has linked to. Wind the camera if it hasn't been already. Make sure the selector around the film winder is on A, not L. Push the shutter release down, and the shutter should fire.
What Rob is describing is known as the "Canon cough" or "Canon squeal"; I prefer the latter as it describes it better. It involves a lubricant drying up, a lubricant which ensures that everything works silky smooth so obviously it is an important thing if the squeal/cough is present. There are audio examples on YouTube, if you need a reference.
If the camera has been well looked after but at the same time used lightly, you might not have any squeal/cough at all - I had an AE-1 Program that was completely free of it, because of this.