How does someone go about placing their mother into a nursing home because she has dementia/Alzheimer’s?

I see you live in OH, too bad it's not NE OH, then the process would be much easier.

Competition for residents for these facilities can be intense.

There are many things that need to be done before having your mother placed in a care facility. First, is she still her own person or has someone been legally appointed as her decision maker? That will determine the next steps. Also, figuring out what her insurance will help pay for, what will need to be paid for out-of-pocket(if any), and finding a facility that meets her particular needs. If safety is a concern, looking for placement in a memory care facility or one that has a memory care unit might be best.

Do you have POA?