You set the Aperture priority mode by using the camera menus on its LCD in which case you need to browse and choose Aperture priority from the menus or by rotating a modes dial in which case you choose Aperture priority by its symbolic icon (in most cases Aperture priority is symbolized by a capital ‘A’).
In Aperture priority mode you manually set the aperture value. The camera takes care of everything else – for example it sets the optimal shutter speed for the aperture you chose. There are physical limitations and not every aperture value that you choose can be matched by other settings that will result in a good photo. The camera will let you know by flashing a green LED or in some other way (check its manual for more details) if it found the optimal settings that work with your chosen aperture value.
So why bother setting the aperture value manually when you can have the camera set it for you? One good reason is to control the depth of field. Depth of field is defined as the range in which the photo is in focus. For example an infinite depth of field means that the photo is in focus from a certain distance from the camera and up to infinity. A narrow (also known as shallow) depth of field on the other hand means that the photo is in focus only from a certain distance from the camera to another distance which is not further away (or in other words the photo is in focus just around a certain object that is being photographed). The rest of the objects in the photo are out of focus appearing as blurred objects.
The wider the aperture value (the f number decreases) the narrower (shallower) the depth of field and vice versa: the narrower the aperture value (the f number increases) the deeper the depth of field. Just remember that the depth of field changes along with the f number: when the f number increases the depth of field increases and vice versa. A common use for manually controlling the aperture value and achieving a narrow depth of field is when taking portrait photos and trying to blur the background behind of the portrait object.
As always the best way to understand what you can do with different aperture settings is to experiment. In this way you will get a feeling of what aperture values translate to what depth of field. It is important to understand though that the depth of field depends not only on the aperture value but also on the object distance from the camera and the lenses that are used. With digital camera experimenting is free and immediate as there is no film development cost and you can review your photos instantaneously.