A guardianship, sometimes called a conservatorship, gives you the legal right to make necessary decisions on behalf of an adult child who cannot live independently. It allows you to oversee
How do I set up a business as a guardian for the elderly? or personally be responsible for the child's care, custody, and control. But laws in every state provide specific criteria for evaluating whether a person qualifies for a guardianship -- and you were right in intuiting that this legal arrangement requires some paperwork and a court hearing.
Whether you may need to hire an attorney for help with this process depends on where you live. Courts in some locales have established some very good self-help centers that provide necessary forms and instructions for how to complete and file them. Find out by doing a search of your city or county and the words "conservatorship" or "guardianship."
If your court does not provide good help, or the idea of going it alone just seems too overwhelming, you should be able to get referrals for experienced legal help through either the National Down's Syndrome Society or The ARC.