How to deal with staff taking care of a loved one who has been admitted to a mental health facility?

Depends on the issue: Generally, the staff need to be dealt with respect and politeness -- these qualities usually bring more results. Is there any particular issue you'd like to address with the staff? If you want diagnosis or treatment related info, your loved one or his/her power of attorney or legal guardian will have to sign consent. The question is too broad and needs to be more specific for a specific answer.