Door knobs are relatively simple mechanisms. Door knobs use a piece called a tongue to hold the door closed. When the knob is turned, the tongue is pulled into the door and the door can be opened. If you turn the knob and the tongue does not pull into the door, the door knob is broken and will need to be removed and replaced. Try jiggling the door knob to see if that will allow the tongue to move. If that does not help, the entire knob mechanism will need to come out.
Place the head of a screwdriver into the hole of one of the screws. Twist the screwdriver counter clockwise to remove the screw. Repeat with the other screw.
Pull the handle off the door. Locate the opening on the top of the latch assembly. Push the end of the screwdriver into this opening. Apply light pressure and push back, toward the door hinges.
Push the door open while applying pressure to the latch assembly. Once you have the door open, pull the other knob out of the hole. Remove the screws holding the latch assembly in place and slide it out. Replace the broken door knob with a new one.