Photos, testimony of people who have observed the alcohol abuse, testimony of a doctor or other person with medical knowledge of the alcohol abuse, relatives and friends, in short, whatever it takes to persuade a judge or magistrate. Talk with an experienced attorney for legal advice on the details.
There is no one answer to your question. Proof can come from any source. What will be necessary is for the Court to believe that the child is not safe with the parent and therefore must be supervised.
I agree with both counsels responses. The more third party individuals who can testify to the parent's drinking and how the drinking is effecting the ability to parent the better. Pictures will also help.