Shutter speed is the easier of the two main factors to consider. Simply put shutter speed is how long the camera is open to light. The faster the shutter speed the less light let in and the slower the shutter speed the more light let in (of course, all else being the same).
Now when converting to stops of light it is much easier twice or half the shutter speed is a stop difference.
However, shutter speed plays an important roll. The faster your subject is moving the faster shutter speed you need to freeze the subject in the photograph, otherwise the subject will blur (which may be an effect you want). Another time you want faster shutter speeds is when you use longer focal length lenses (that is lenses that bring distant subject closer to you). Longer focal length lenses shorten the apparent distance between you and your subject, but they also magnify shakes and other movement. The rule of thumb to remember is for instance, if you are using a 200 mm lens you need to shoot at 1/200th of a second or faster to hand hold.
When you use slower shutter speeds you can use smaller apertures thereby increasing your depth of field.
Next installment putting it all together.