A simple hook and latch lock helps a screen door from blowing in the wind or being pushed open by a child or pet. It doesn't offer much security against a home invasion, but it is simpler to install than other types of locks. An eye bolt is embedded in the frame of the screen door, then the hook is attached to the door frame on the wall. Latching the hook into the eye bolt keeps the screen door shut.
You may use a handle and lock mechanism if the door frame is wider than the lock mechanism you wish to install. A hole must be drilled through the screen door frame where you want the lock to go. The door handle installs through the hole. Locking handles need a plate installed on the door frame around the screen door for the bolt to slide into. Look for small door handles designed for use on screen doors instead of trying to fit a full sized door knob on the frame.
If you want to lock your screen door from the outside and open it with a key when you return home, you'll need either a tulip knob or a push button lock, according to Zipf Lock Company. The tulip knob is shaped like a normal interior door knob with a key hole in the middle. The push button lock is the same vertical handle that many screen doors use, but with a key hole added to the handle or the push button.
Chain locks are convenient and easy to install locks that work fine on most screen doors. A small metal stopper, attached by a chain that is anchored on the screen door frame, slides into a metal bracket that prevents the door from opening further than the length of the chain, reports Locksmith Tool and Supply. Two screws hold either part of the lock to the screen door frame and the wall.