What makes one eligible to enter a nursing home?

How is the decision made as to who makes the call to have a loved one enter a skilled nursing facility?  What makes one eligible to enter a nursing home?  How does the money work - with  medicaid, etc.?  At what stage do you go from Assisted living to a skilled nursing?  If we have no more money for medical - emergencies, etc., does medicaid cover expenses?  Thanks.