After you have arrived at EZEIZA airport (real name: Ministro Pistarini), you will feel as in the middle of the "pampas"!!!   Well... yes, it is: you're 25 Km.(14 miles) from the city. There are diff. ways to go there:

Shuttles:
Several bus companies: Manuel Tienda Leon, San Martin, Transfer Express, runs hourly (until 10 PM) and make a non-stop trip straight to north downtown. Cost: about $100.

Taxis:
There is a desk in the hall and others outside the building. Trip: about $150 Don't take a taxi that hasn't been called from a desk!. Also the driver could try to take advantage of you by demanding money for carrying extra luggage.
Remises (private car rentals) are called in the hall. Be careful. They cost less than taxis but just in case remember to take down the plate number. It is normal that you pay the tolls ($5).

Local Bus (8 line, former 86 line):
If you have time, not too much baggage, and you speak some Spanish, you can take a bus to my guest house, or to downtown. Buses leave every 15-20 minutes (from 6 AM to almost midnight).
There are two bus stops outside. The nearer is, once you leave the main airport building, at your left, after the last pink building. Ask at info desk.

Tell the bus driver that you are going to "Caballito" (to my house), or "Centro" (downtown), and relax: you will have a nice, long one-hour travel from the surroundings untill the heart of the city. Cost to my house: $2
You will need coins to pay in a machine inside the bus. To change money, Banco de la Nacion (main hall) has better rate than at the private change desks.

Since Ezeiza is the departure point, the bus will be empty. Try to sit near the back door to exit easily with your baggage. There could be plenty of people on the bus when you have to get off.

Bus take the highway with a few stops in small towns on the outskirts When bus gets to Rivadavia Av. you are entering BA!! At last!!

To my guest's house: get off in Rivadavia 5,900 (the blocks go by 100's). Ask me for further directions.
To downtown: some minutes after the bus leaves Av. Rivadavia, it will turn onto the Hipolito Yrigoyen St. In 20 min more, at the 1,900 block, you will see (to your left) the Congress building and a park: it's the beginning of downtown. At the 300 block you'll arrive at Plaza de Mayo (downtown core).
     NOTE: Some buses (branch "S") takes a direct highway to Congreso. Cost is higher. They DON'T pass for my house.

This will be the end of your first adventure in BA !

Guest's tip:: I use to pick my guests up for just the cost of tolls, gasoline and airport parking (U$S 20).