Begin by determining how far from the floor the dog door will need to be. Generally speaking, you want to position the dog door so that the bottom is nearly even with the bottom of the chest of the dog. From that point you can use a tape measure to determine how high the top will go on the door. You should try to keep the doggie door centered on the storm door. After you have marked the bottom of the door, it needs to be removed for cutting. Take a hammer and flat head screwdriver to pry the pins out of the hinges. Take the door off and take it outside.
Once the door has been removed you will need to set it up on sawhorses or some other supports. You need to draw the outline for the cut. Use the measurements provided for the dog door frame. Some dog doors will have a template but if not you can use a square and tape measure to draw the outline. Cutting the storm door is actually very much the same as cutting a wooden door. The main difference is in the bits and blades used. Use a metal drill bit to drill a hole in each of the four corners for the dog door. Use a small bit initially, making sure not to dent the door. Increase the size of the bit and widen the holes. Continue this until the holes are large enough to turn a jigsaw inside without hitting the edges of the hole. Put a metal cutting blade on your jigsaw to cut the outline. Begin in one corner and continue around the form.
Installing the dog door frame will also be slightly different with a storm door. Because there is another door inside of a storm door, caulking is not necessary and is not practical on an aluminum door. You will position the frame in the opening in the same way as you would with any other door. It is important to make sure that the hinges on the dog door open upwards and are on the inside of the door. You need to replace the supplied wood screws from most dog doors when using aluminum. Purchase sheet metal screws or you can even use small bolts. If using bolts drill the holes through the door and attach the bolts. For sheet metal screws, simply place the driver bit on your drill to attach them.
You can then reattach the storm door to its hinges. Use a hammer to re-secure the pins. Test the dog door to make sure your dog is comfortable using it. You may have to work to train your dog to use the dog door but most dogs can figure it out fairly quickly. Many doors will also come with a security insert that prevents outsiders from unlocking doors through the dog door. While this is an important feature, it is not as crucial on a storm door and you may choose not to use it unless you will be gone for an extended period.