My grandmother has dementia and only receives social security. She has no assets and she needs full time assistance. What do I do?

Terrific answer, Lilliput. Many elders who only get Social Security qualify for Medicaid. Generally, the County Social Services office will handle this. People can go to their state website, type "aging" in the search box, and a link to the state's Medicaid information should come up. While Medicaid is a federal program, each state handles it a bit differently.
Take care and good luck with your grandma,
Carol

She may be eligilbe for Medicaid funds...it sounds like she would qualify by income. Contact your grandma's doctor or call your local hospital and speak with a social worker who can get you started on applying.
Was she or her spouse a veteran? There are some funds available there too.
Group homes, as opposed to ALFs or NHs, are a little less expensive and many cater to Alz. residents.
good luck

If all she has is SS under $ 2,000 a mo, then she will qualify financially for medicaid.

But you will need to have her doctor work with you to have her qualify medically for Medicaid too. At 77 she is somewhat young for long term care so her medical needs will have to be documented with a medication & illness history that will need skilled nursing supervision.

If she doesn't have a detailed medical history of serious health problems at 77, then you will need to get one going. If this is the case, here's my suggestion:

I'd approach it somewhat differently in that I would find a place for her - whether is is a board & care home, group home, nursing home - that you like for her and that takes residents "Medicaid pending". This is really important as the Medicaid processing takes a while and you want to limit her & possibly your debt to whatever her SS check is less $ 60 for her montlhy personal expenses.

Find out who is the medical director for the facility you select and make an appointment for granny with him. Be sure you tell her current MD that you are doing this as you will need to have a copy of her medical history sent to the new MD. The medical director will have a better idea of what to indicate for her diagnosis, medications and other needs that will pass Medicaid medical review.
As he will be her new MD, this will make it all easier for everybody later on.

One thing that happens often for elderly living with family is that they aren't on medications that require skilled monitoring or assistance in use (like the Exelon patch) or they refuse to take medications so the prescriptions haven't been filled so they move into the NH without any medications or family has been doing things for them so there is no medical history of falls or burns or other illness other than general aging. Then something happens, like the heart attack of her caregiver, and granny has to get into a NH asap. So they go into the NH with no real prescriptions or diagnosis and then they are denied Medicaid as "not medically needed".

Most of this site's info on Medicaid is all about how to qualify financially but the medically necessary aspect of Medicaid is just as important. Good Luck!