My father-in-law has Alzheimer’s and dementia has not decided on a guardian. How do we get him to set up guardian or Power of Attorney?

It is correct that a mere diagnosis of Alzheimer's/Dementia is not an automatic determinant as to "cognitive capacity". It is also true that a diagnosis (and especially if the elder is already in a nursing home) can be grounds for challenging the appointment of a POA.
Before you start running to lawyers to establish guardianship, let's figure talk about why you need a POA.
A Durable Power of Attorney will permit you to handle financial and contractual matters only.
Health care matters you already have proxy for and that is really important given your FIL's situation.
But, if has already signed for financial responsibility for the nursing home, and if you have joint ownership of any remaining assets, a POA may not be so important if all other financial moves have already been made (property ownership, insurance policies, etc.).
Your sister wants to move him to TN. That sounds like a health care decision, not a financial or contractual decision.
I would simply let him know that you already have the power to assist him with health care decisions and it will be foolish not to allow you to help with financial matters. Explain once more that if he does not do this voluntarily at some point the State will be asked to appoint a guardian for him and it may not be you!.
Will he prefer a stranger handling his affairs?
If he doesn't budge, well then so be it. At some point he will indeed become so incompetent that the nursing home or social services will have to apply for guardianship. Let them do it. Then the fees will not be yours to pay.

Is there some reason he won't sign, or is it because he can't sign? If he just will not sign out of cussedness, then is there someone closer to his age that might talk to him about it? If he's able but unwilling to sign, has anyone asked him why not? Is he afraid that signing POA will somehow guarantee he's going to die or that it's like he's losing control forever? Even if you were to go to court and get the rights to do the POA thing, aren't you going to have a problem with the sister-in-law that wants to move him? What does your husband say?

NO!

If the elder has been diagnosed with dementia and it is documented in their medical history, then they legally cannot enter any agreements (like a DPOA, or will, etc.) as they do NOT have the cognitive skills needed to make such a decision.

If you get them to sign DPOA, etc., and another family member challenges the documents, you could find yourself in a whole packet of legal problems. Sounds like your SIL and you are not on the same page for his care, if that is the case you are just asking for trouble if you make him sign anything.

This is why it is just so critical to get things done way in advance.

Unfortunately if you don't do advance planning, you will need to go the route of getting Guardianship/Conservatorship for your FIL in court.

This is sticky, you'll need to hire an experienced lawyer to help. To begin your search for the best lawyer for the job, contact the local bar association and ask whether it has a lawyer referral service that includes those who specialize in conservatorships or elder law. You can also contact the National Academy of Elder Law Attorneys for a referral to its members in your area. Good luck.

He wont sign it because hes being honory. Hes stubborn and set in his ways......He says everyone steals his money etc....Not true. He is able to sign just wont to be a pain in the ass to the rest of the family. Ive had the Social Worker at the Nursing Home talk to him and that didnt help at all. Im at a loss on what to do in this situation. My husband says nothing as it is his step father so he really doesnt care anymore.

Again, if he has been diagnosed with Alz & dementia & is in a NH, then because of his illness he DOES NOT have the cognitive skills to legally enter any agreements. Any legal documents done can be challenged as a "coerced document". If you benefit from it and it is challenged by your SIL, then you could face elder abuse charges. This is pretty serious.

The fact that your hubby doesn't want any part of it, is not working in your favor
either.

My husband signed POA and Medical proxy and other papers after he was diagnosed with dementia. This was done under the guidance of an Elder Law attorney. She even offered to come back if the appointment time found him confused. (Lewy Body Dementia has periods of being perfectly lucid alternating with cognitive impairment. She wanted to be sure he signed in a lucid period.)

Since "dementia" covers such a wide range of impairments and loss of skills, it is hard to see how it would automatically disquality any one from signing legal documents. In Wisconsin, for example, a recorded diagnosis of dementia is not even grounds to automatically dismiss charges, for example if a demented person in a nursing home harms someone else. I wonder if this varies by state?

In any case, FIL does not want to sign, so even if he legally can in his home state, it hardly matters. But if no one has POA I don't see how the SIL could have him moved -- unless FIL wants to move. And if he does, what is the fuss about?

By the way, Alzhiemer's Disease IS a form of dementia, so a diagnosis of Alz automatically means dementia. You can be diagnosed with dementia and not have Alz (for example, you might have Lewy Body Dementia), but you cannot be diagnosed with Alz and not have dementia.