If your sister is an adult, you would file a petition for conservatorship. If she is a minor, you would file a petition for guardianship. Different terms, similar concepts. Either way, you file the petition and lots of supporting papers in the probate court of the county in which your sister resides. After you file the appropriate papers, and family members are given notice, the court will hold a hearing to determine if it is appropriate to appoint a conservator, as well as determine who should be appointed. A court investigator will also conduct an investigation and make a report to the court. If you are appointed, then you will have legal authority to make decisions for your sister, and if you are appointed as conservator of the estate, you will have the authority (and responsibility) to manage her financial assets as well. One caveat, however, the courts are not generally inclined to appoint an out-of-county or out-of-state conservator if there is a better, more local option, but that being said, it is also possible to get appointed and then seek court approval to relocate your sister to your state, if that is appropriate for her.
The conservatorship process can be challenging to someone not familiar with the law and applicable procedures. You should consider consulting with an experienced conservatorship attorney who practices in the county in which your sister resides.
This general response is not intended to create an attorney-client relationship.
As noted above, you will need to file court pleadings and will require the assistance of a California attorney who is thoroughly familiar with the rules in her county. If the State is already involved, time could be of the essence, so I recommend you confer with legal counsel at your earliest opportunity.