In a DSLR camera is it possible to view the image you are going to take on the LCD screen or only through the viewfinder?

yes for both digital compacts and slrs - i use both methods of viewing depending on circumstances - using the lcd is great for shots that are at weird angles or if you need to hold the camera very high or low - the viewfinder i find is best for fast action shots that need to be panned or tracked - since i started with old style film cameras i tend to use the view finder more but those who start with a digital tend to use the lcd screen more