Deadbolts add an extra level of security to doors, because they are often more resistant to blunt force and lock picking. As part of the security features, there are often no visible screws on the housing of the deadbolt and key tumbler assembly. Companies like Schlage make various sizes and types of deadbolt housings with no visible screws. However, if you need to replace the deadbolt, you can in fact remove it yourself if the door is unlocked to begin with.
Inspect the front of the deadbolt. Look for a seam along the circular edge of the deadbolt keyhole front panel.
Insert the tip of the screwdriver into the seam and gently pry the front plate off to reveal the screws. If you do not see a seam and the "cap" over the key hole and body of the deadbolt seems to be one piece, skip to Step 3.
Insert the tip of the screwdriver between where the metal of the deadbolt housing meets the door itself on the front of the door. Gently pry around the edges of the housing until it comes off to reveal the screws.
Use the Philips-head screwdriver to remove the exposed screws and remove the keyhole housing, which contains the lock tumblers. You may need to repeat these steps on the inside of the door if the deadbolt mechanism does not come out of the hole in the door.
Open the door and remove the screws holding the bolt's plate in the side of the door. You may need to lift out the bolt itself, either through this side hole or lift it out of the hole now visible when removing the housing of the key and locking mechanism.