A telescope's magnification is actually a relationship between two independent optical systems–the telescope itself and the eyepiece you are using. To determine power, divide the focal length of the telescope (in mm) by the focal length of the eyepiece (in mm). By exchanging an eyepiece of one focal length for another, you can increase or decrease the power of the telescope. For example, a 20 mm eyepiece used on a 1000 mm focal-length telescope would yield a power of 50x (1000/20 = 50) and a 10 mm eyepiece used on the same instrument would yield a power of 100x (1000/10 = 100). Since eyepieces are interchangeable, a telescope can be used at a variety of powers.
There are practical limits of magnification for telescopes. These are determined by the laws of optics and the nature of the human eye. As a rule of thumb, the maximum usable power is equal to 50-60 times the aperture of the telescope (in inches) under ideal conditions. Powers higher than this usually give you a dim, lower contrast image. For example, the maximum power on a 60 mm telescope (2.4" aperture) is in the range 120x-142x. As power increases, the sharpness and detail seen will be diminished. The higher powers are mainly used for lunar, planetary, and binary star observations.
Most of your observing will be done with lower powers (6 to 25 times the aperture of the telescope in inches). With these lower powers, the images will be much brighter and crisper, providing more enjoyment and satisfaction with the wider fields of view.
A good way to increase magnification is to use a Barlow lens. A Barlow lens rated at 2x can be used with your existing eyepiece and it will double the magnification of any existing eyepiece.