What is the procedure to get someone declared mentally incompetent in California?

Have your POA reviewed by an attorney. You may be able enact your power with a simple letter from a doc stating that she is incompetent and cannot handle her affairs. Do it soon. Hubby sounds pretty dodgy. Get control of her finances and property for her care.

Honestly you need to see an Elder Law Attorney. This is too complicated with a living husband that she never left, though she apparently thought to make you POA for both health and financial. Showing signs of dementia is not diagnosed medical dementia. You need the guidance of an attorney. And becoming her guardian will involve the law. It is very likely that you will win guardianship if her husband asks for it, I believe, as there is no record of her wanting to leave him I am assuming. This is not going to be easy, I think, but an attorney would know bushels more than I do.

Even though my sister is married, her husband has been less than stellar in his treatment of her. He's a narcissist and we are worried that he doesn't have her best interests in mind. She has some property in her name only that he wants to sell and if that happens, we need to see that the money stays hers and not spent by him. It's a very complicated and sad situation (their relationship) and at this point he is in even more control than when she was functioning mentally.

Why do you wish to have her declared incompetent? Are you unable to help her make decisions for her own safety at this point? You are already acting as her power of attorney for all care?
If you need guardianship for placement then this will go through an elder law attorney who will file in court, and the court will rule based on her medical doctor's assessment, and etc. but the attorney will guide you through it. It will entail a court procedure.
Be very certain that you actually WANT guardianship; it is a massive undertaking mentally and emotionally and time wise. This will mean that whoever is appointed, you or your neice, will be filing all the papers, and paying all the bills and getting all the medicaid documentation, etc. If you do not wish to take this on then ask that the court appoint a fiduciary to manage money and continue to do the medical power of attorney or ask that there be a court appointed guardian. If the neice wishes to take it on perhaps you can help her with it. Good luck.