It is not that easy. You need to be certified to adopt. And...there is the issue of the putative father. Your friend needs to contact an attorney that handles these things issues. I am not sure of an attorney in Graham County who could advise, but there are certainly good adoption attorneys in Pima and Maricopa.
This general information does not create an attorney client relationship between the questioner and the author. The internet is NOT a place to get 'legal advice'...although gathering general information is always helpful.
It is great that you are agreeing to take parental responsibility of the child. The immediate problem you have is the father. That person has parental rights to the child. Get an attorney to help you through the process.