Crop sensors are smaller than full frame sensor. The full frame sensor size came from the old days and has been used as a standard for digital sensors size.

From Wikipedia

Crop factor is related to the ratio of the dimensions of a camera's imaging area compared to a reference format; most often, this term is applied to digital cameras, relative to 35 mm film format as a reference. In the case of digital cameras, the imaging device would be a digital sensor. The most commonly used definition of crop factor is the ratio of a 35 mm frame's diagonal (43.3 mm) to the diagonal of the image sensor in question; that is, CF=diag35mm / diagsensor. Given the same 3:2 aspect ratio as 35mm's 36mm x 24mm area, this is equivalent to the ratio of heights or ratio of widths; the ratio of sensor areas is the square of the crop factor.

So to determine your crop factor, you need to know your DSLR sensor size. It's 1.5 for Nikon, 1.6 for Canon, 2.0 for Olympus, 1.5 for Pentax and 1.5 for Sony.

To calculate the effective focal length or the focal length multiplier, use this formula:

focal length multiplier = focal length x crop factor.

For example, let's say that your crop factor is 1.5 and your lens's focal length is 50mm, then the focal length multiplier = 1.5 x 50 = 75mm.

Bear this in mind: the physical focal length of your lens didn't change at all. What you see in your photo is the effect of your crop sensor, let me explain more:

Look at the image below, the red rectangle is for the full frame sensors, now if you are using a lens on a full frame camera and used 50mm lens to get this picture below, the photo will be everything inside the red rectangle. If you replaced your lens with a 75mm lens you will get a photo with everything inside the blue rectangle. Which is the same if you mount your 50mm lens on a cropped sensor camera with crop factor = 1.5

Crop Factor doesn't enhance the zoom, it just gives you the field of view that you would see if you zoomed more.

The image below is from this Wikipedia article.