I have some DEMs and have computed the slope in degrees for each one. I have also classified the slope raster into the following 5 classes: 0-3, 3-15, 15-35, 35-50, >50. What I want to do is to calculate the area that has, for example, slope inside the 0-3 degrees class.
One way to get an area by doing a little manual work is to open up your DEM properties window on the symbology tab. Click on Classify... and click on your class break values in the window on the right. There will be an "Elements in Class" number on the bottom right of the window which is the number of pixels in that class. You can then multiply that number by the area of each pixel (ie/ multiply by 900 for a 30 x 30 pixel size). This will give you an area for each class.
If you have a Spatial Analyst license, then you can Reclassify the slope raster into five classes (0-3, 3-15, etc.). Then, the raster's attribute table will show how many cells are in each class and the area can be easily calculated.
If you don't have the license or don't want to make a new raster, then Calavin's suggested method is ideal.