Storm doors tend to stick more often than regular doors because they're not as solid and they're on the front lines of the weather year-round. When you find that your storm door isn't closing properly, it could be from any one of several issues. The good news is that it's often just a matter of adjusting the hardware and tightening the screws. Always, try the simplest solutions before moving onto the more complicated ones.
Open the door, find the closing mechanism (the cylindrical tube on the hinge side that prevents the door from slamming shut), then find the door-stop mechanism next to it. It's the small, flat piece of metal on the closing mechanism, about the size of a postage stamp, that can slide forward and back. Slide it as far toward the hinge side as it will go, so it's not holding the door open at all.
Adjust the closing mechanism itself if necessary. Most are designed with an adjustment screw at the end of the cylinder that points away from the hinge side. Using your screwdriver, turn the screw counterclockwise to decrease pressure inside the mechanism. This allows the door to close faster. Make the adjustment half a turn at a time, testing the closing rate of the door each time. If you overdo it and the door now slams shut, adjust the screw slightly clockwise to increase pressure.
Check the latching mechanism for any raised screw heads that are preventing the door from closing. If so, turn the screws clockwise to tighten them down to the surface.
Stand outside the storm door and open it wide enough to look at the hinges and the metal frame that's attached to the door jamb. Press on the narrow outer edge of the door, and watch to see if the frame moves at all. If it does, secure it by tightening all screws, clockwise, into the door jamb. (Note: If your door doesn't have a metal frame and is hanging directly on the wooden door jamb, you can drive a few nails directly into the jamb to tighten it.)
Using your screwdriver, tighten all the hinge screws, turning them clockwise. If they spin in their holes without gripping wood when you try to tighten them, it means the screws or screw holes are stripped. Take the screws out and replace them with longer screws that can reach deeper, to solid wood. (Note: To get stripped screws out, press the edge of a putty knife under the screw head to give the screw threads something to grip, then turn counterclockwise.)
Push on the other jamb of the doorway (on the side where the doorknob lands) to see if it's loose. If so, tighten or replace any screws as necessary, or put in a few nails if it's wood.
Visually assess whether the structure of the door itself is "sagging'' at the corners, so that it is no longer in line with the door opening. This is a common problem with older wood storm doors, and it's generally more trouble to fix than it's worth. At that point, you might be better off just getting a new storm door.