Summarize:

Though you don't need much to create a the basket, it will come together very quickly if you find all the parts before you start. You will need: A wire hanger. It cannot be a partially metal hanger made substantially of wood or plastic. A large, flat piece of cardboard. The tape of your choosing. Marking tape may be the easiest to work with; duct tape would certainly make the hoop durable. Markers or paint. Scissors. String (optional). You do not even have to dismantle the hanger, but just reshape it into a hoop. Do not cut away the hook, as it still can be of some use. Standard high school, college, and NBA backboards are rectangular, if you are looking to replicate that appearance. Try to make sure the relative scare of the hoop and backboard seem reasonable. For comparative purposes, an NBA backboard is 6 feet wide, while the basket opening is 18 inches (1.5 feet). That means the basket width is 1/4 (or 25%) as wide. Traditional hoops are painted red, but you can certainly customize it to fit whatever you desire. The backboard of most high schools, colleges, and all NBA franchises are now made of transparent glass; as there is no transparent cardboard, you can really be as creative as you want. You can attach the hook (which you bent up earlier) to lower back side of the backboard. Make sure the rim is as close to the backboard as possible. You can make make a net out of string, or even out of twisted tape. Masking tape will work well for this purpose, as it will not leave a sticky mess behind like duct tape would. There are two different taping methods you can employ. You can tape along the front perimeter of the backboard and extend the tape onto the wall to secure it. Alternatively, you can make tape hoops (by attaching a single piece of tape to itself, end-to-end with the sticky side out) and use these to attach the backboard to the selected surface.
Obtain the necessary materials. Bend the wire hanger into a circle. Bend the hook of the hanger so that it is at a 90 degree angle with the hoop. Cut the cardboard to the size and shape of your liking. Decorate the hoop and backboard to your liking. Tape the hoop to the backboard. Attach a net to the basketball rim (optional). Hang the completed basket to a wall or door.