How does one begin the legal process of having a person declared incompetent and have a guardian/pay

Well the very first step is to arrange a consultation with a lawyer. Just pick a lawyer out of the phone book, arrange a meeting, and explain your case to him/her. Tell the lawyer why you want to have this person declared incompetent and what evidence you have of this. The lawyer will tell you what to do from there.

Having someone declared 'incompetent' is all a bit 20th century. The modern approach is a little different.

If the individual concerned has ever made an enduring power of attorney or a lasting power of attorney then the attorney(s) are the person(s) who have been appointed to manage the individual's affairs. The power of attorney must be registered with the Court of Protection before it can be used.

Otherwise, you will need to apply to the Court of Protection to be made a 'deputy'. HM Courts Service leaflet COP42 provides a good deal of information about this. A link is here:
http://www.hmcourts-service.gov.uk/courtfinder/forms/COP42_web_0409.pdf