Depends on how far along the person is. If the person has periods of lucidity where he or she knows what she is signing an why and there are independent unbiased witnesses who don't have anything to gain, then it might be possible.
On the other hand if the person is already in advanced stages you will have to apply to the courts for conservatorship.
The one and only way to obtain a power of attorney ("POA") is for the principal to sign it (if you don't know what a "principal" is, read this explanation of the basics of powers of attorney). If the principal is not competent to sign a POA, then you can't obtain one and will need to seek a conservatorship through the courts.