Aperture is the size of the hole letting light in or the intensity of the light during the photo. A wide aperture results in a sharp image around what the lens is focusing on, which is good for wildlife or sports photography. A narrow aperture lets in less light and is useful for landscape photography because it creates a sharp focus on all the objects within the frame.
Shutter speed is the exposure time of a photograph. A fast shutter speed will capture a moving image quickly and combined with a wide aperture focusing on a subject, will create a sharp image of a moving athlete or animal. A slow shutter speed (obviously) takes longer for the exposure, and wouldn't be ideal for sports or animals where there is constant movement. This would make the image look blurry. A slow shutter speed and a narrow aperture are the setting ideal for a landscape because with the narrow opening you get a sharp focus on the entire image and the slow shutter speed allows enough light to get in through the narrow opening to catch the image.
The general rule of thumb is the wider the aperture the faster the shutter speed and a narrower aperture calls for a slower shutter speed.
Digital cameras have made this easier on photographers in many ways. One thing that you get with digital is the histogram which can give you instant detailed feedback on the accuracy of the exposure for your photos. The histogram graphs the luminance values in the frames and will give you advice on how to adjust the aperture or shutter speed if need be. Practicing on landscapes until you get this down is advised because if you are trying to capture wildlife such as a flying bird you may not get a second chance for a shot. Knowing how to use your equipment and what you want to shoot are also very important for getting the perfect exposure.