You will need your passport ( current ) a copy of your certificate of completion of high school and that copy needs to be validated. The validation of the secondary studies degree which must be processed at the Direction of Validations of the Ministry of Education, Science and Technology (950 Montevideo St. - every day from 10.00 to 12.00 and from 14.00 to 16.00). Once you have that you can go to Secretary of Academic Affairs. The enrolment procedure is to be started at the Direction of Degrees and Plans (950 Uriburu St. , 1 st floor) on Mondays and Thursdays from 12.00 to 16.00.
The CBC is the firs year for any career you choose to study. Typically there will be assigned dates for enrollment based on your last name initial ( for example you will see signs that announce "a-d 5 de julio" ) so you must go on that day to enroll to your classes. You will have different options for UBA locations based on the career you chose and the classes you want to take. Once you do this, you have to look for the dates they will publish the lists with assigned hours, locations, etc ( you will find that sometimes they do not match your choices or you can´t find yourself on the lists ), the lists are literally hundreds of pages they stick to the walls with all the results, etc. You will have a second chance to make another selection and that is it.
The CBC gives you the choice of two classes that you can study in distance learning format, that is a whole separate procedure with separate books, etc.
Once you are done with the CBC ( and please always ask for proof of the classes you passed as sometimes they get lost and you have to do it all over again. Proof can be a simple form with a seal and or signature expedited by the CBC ) you get enrolled into the career of your choice ( notice that each career is taught at a different building ). The process to get enrolled to each class is similar to the CBC, but it happens that that one building. You will need to apply for your UBA student booklet and make sure it gets stamped with every class you complete.
Okay these are the basics, remember that UBA can get very burocratic so be prepared for that, in a few months you will be amazed at how you got used to it! I am not sure they have an English speaking person at Uriburu 950 or anything in English, so you might want to go with a friend if your Spanish is not very good. The buildings can be dirty, cold, etc, don´t give up, but keep your expectations to a realistic level
If you want you can just go into any of the UBA buildings, even go sit in a classroom and see how you feel there ( nobody will ask you anything and it is actually a good test drive )
http://www.uba.ar/ingles/studying/requirements.php
Hope this helps!