I went with my oldest girl to ACA about 5 weeks ago to look at all of this. Of course, me being over 50, I seem to have a mild form of Alzheimer's and couldn't remember things for sure, so I went to ask her just now to help me remember
ACA will handle everything. You pay their monthly membership fee, which is something $400 to $600 pesos a month (it was more for me at 52 than for her at 19). They have a class for theory and for practice, they give the tests, both written and practical. As I and my oldest girl remembers, they do everything to get the license. It was one of the reasons that I considered going there to pay at least a month or two of monthly dues to get my license instead of going through the bureaucracy of CABA to get my license.
As we remember it, paying the monthly dues for ACA itself gets you into the school, although I think at a discount, not completely free. My girl remembers it being free if you're an ACA member, but I remember there being a discount
Their main headquarters is at Libertador 1850, where we went one afternoon to ask the specifics. Go in, take a number, and sit down and talk with them to make sure what I'm telling you is true.
Their school for both written and driving is located close to their main headquarters (maybe 10 blocks away or so) at Av. Casares 3955. We went there to sign up for the school (from their headquarters it's pleasant walk through the parks, and it's close to the Japanese Gardens, which we went to after finding out I couldn't sign up for classes yet), which was when I found out I couldn't take the tests until I changed the address on my DNI to reflect the fact that I now live in CABA. They also allow drivers to rent a car for the driving test.