It is not an easy process and, unfortunately, one that hits Alzheimer families/carers too late.
It involves a long procedure through the High Court, Family division and is alot more expensive than just a solicitor as it can sometimes involved barrister representation. We had the learning lesson on my grandmother and that cost over £2k several years ago, - we now have PoA on my mother through my sister, having put this in place when she and we were suspicious that she was losing her memory.
Sorry to hear about your Dad and remember there are a lot of us here going through the same experience, so do not hesitate to ask for advice or vent off.
My number one piece of advice is you are caring for him is to make sure you have your own time, even if it just an hour out with friends or a quick visit to the pub/wine bar/wherever.
I am keeping a diary of events etc as to a potential book on some opf the pragamatics and the necessary humour that you need to retain through the sorry process.