Almost all of our serial numbers are located on the bottom bracket shell of the frame. Some newer models will have a non-removable sticker on the down tube near the bottom bracket. Specialized serial numbers typically start with the prefix "WSBC", "WUD", "STT" or "STE".
If you don't know where the bottom bracket shell of the bike is, simply turn the bike upsidedown and the bottom bracket is the part of the frame that the cranks run through. You will see the serial number stamped into the frame down there.