A pesonal story: I was still a noob at FPS games, and hadn't quite figured out how to snipe. There was a sniper and spotter on a hill, tearing us up. I had a sniper rifle, and managed to get out of the spawn. After leaving the spawn, ran around the long way, and came up the back side of the hill. There was the sniper and spotter, only 15 yards away. Got the spotter first, because the assault rifle was a greater threat, then took out the sniper. Once I saw their spot, and how they were using it, my sniping improved dramatically. It took them almost 10 minutes to get me in that spot, and it was the beginning of my succesful sniping in FPS games.
If you know the approximate location of the sniper, you can plan a route that will keep you out of the crosshairs. This will allow you to approach him without being detected, and give you a serious advantage as you get closer.