Is it the siutation that you are thinking that moms level of care is moving past whatever at home or community program (like senior day care) and that she now needs 24/7 care in a LTC /NH facility? If that's the situation, mom is going to need written orders from her MD that skilled nursing services are required. Medicaid is a needs based program both for finances and medical needs. If whatever program she is in presently is telling you that mom needs a higher level of care, they should also be able to give you some sort of document on this as well.
With these, you can start to look to find a NH with an open medicaid bed available. For new to Medicaid applications, the NH should have a sheet that lists the documents required to accompany the application, which they (the NH) in turn submit to the state along with their bill. This is how it ran for both my moms & MILs application. As your mom is already on Medicaid, that might not be needed as she qualifies to be "at need" financially. Then all she would need is to clear the "at need" for ltc medically - which her MDs orders provides as the initial screening. Admissions at the LTC facility usually take the lead on getting the ltc application done; the facility may have a given caseworker for the NH too.
With these, you can start to look to find a NH with an open medicaid bed available. For new to Medicaid applications, the NH should have a sheet that lists the documents required to accompany the application, which they (the NH) in turn submit to the state along with their bill. This is how it ran for both my moms & MILs application. As your mom is already on Medicaid, that might not be needed as she qualifies to be "at need" financially. Then all she would need is to clear the "at need" for ltc medically - which her MDs orders provides as the initial screening. Admissions at the LTC facility usually take the lead on getting the ltc application done; the facility may have a given caseworker for the NH too.