Every state has its own guardianship laws, but they’re all similar. You will have to petition the appropriate court in your brother’s state to be appointed guardian. This is often the local probate court. As part of the process, you will have to produce medical evidence of your brother’s incapacity, usually an affidavit by a doctor, and give notice to your brother’s next-of-kin – his son. Then the court will have a hearing and make a decision.
Moving your brother to your state is a whole other process. You may need first to get permission from the court in your brother’s state. And once your brother has moved to your state, you will have to initiate guardianship proceedings there and ultimately file the necessary reports and papers to terminate the guardianship in the original state.