Find the best place to mount the basket on your power chair. Make sure not to block your view of the ground if you choose to mount it on the front. On the back of the power chair look for metal poles or sturdy platforms that can support a basket. Size out a basket for your power chair. One that is too big will be hard to mount and may be at risk of falling, while a small basket has limited usefulness.
Use duct tape (colored if you wish) to fasten the basket to your power scooter. Duct tape is strong enough to hold it up and will resist at least some water damage. It is also very easy to replace, simplifying repairs. Cut slits in the wall of the basket that will be fastened to the power chair. Pass tape through slits and around the mounting surface to secure the basket. Secure the top of the basket first. You may need to use a lot of tape to keep the basket steady.
Test the basket's strength by filling it with books, groceries, garden tools or other common items. Find a more stable spot to secure the basket and use more duct tape if it falls.