Although in many places you can pay with American Dollars (and, more rarely, in Euros), you will find that the exchange rate might not be the most convenient for you, unless you ask for the "informal" exchange rate that local people use if they want to buy dollars (because of currency restrictions and controls imposed by the government).
Purchasing something at a store and paying with dollars in excess of the purchase amount might be a reasonably safe way of getting change in pesos at a realistic exchange rate. As of September 2014, the "informal" rate is about 90% higher than the official exchange rate, close to 16 pesos per dollar. Try to get some pesos as soon as you get to Argentina. Buses do not accept foreign currency. Taxis and shops might accept U.S. dollars, and they should give you a realistic exchange rate, but that can involve some negotiating.
Banks & Currency exchange
Currency can be exchanged in most Banks (open from 10 am to 3 pm) and exchange companies "casas de cambio" operating in the same time-range, but only at the official exchange rate. Be careful exchanging your money with people in the street, operating mainly in the downtown area (called "arbolitos" -little trees- by locals, since they are right beside the road and are full of "green" leaves) even though they will quote you the higher "informal" exchange rate. If you do use them, try to exchange a small even number such as $100 to make calculations easier (some are known to use "fixed" calculators in order to pay you less money).
If you arrive to Buenos Aires by plane, there is a branch of the Banco de La Nación (state owned bank) located in the arrivals area of the airport which will exchange your currency at the official rate.
You can always exchange dollars at the official rate in several Banco de La Nación branches or at exchange bureaus across town. Another alternative is to get local money from your account using the ATMs spread all over the city, but again, you will then get the official (much lower) rate.
ATMs are found not only in banks but also in Shopping Centers (such as Alto Palermo, Paseo Alcorta, Unicenter, etc.) and many large supermarkets (Jumbo, Disco, etc.). The largest network of ATMs is Banelco. In the web page you can find an ATM locator. The web page is in Spanish, unfortunately. Beware of the credit card rates.
Be advised not to exchange more money than you will need, because it has become almost impossible to exchange any leftover Pesos when leaving the country.
Black Market (Dolar Blue)
Due to problems with inflation and the fact that the locals find it very difficult to obtain $ dollars there is a flourishing black market for $ dollar bills. The $50 dollar bill is the most popular and gets the best rate, they are not interested in anything lower than $20. In many places you will find shops and restaurants that will offer you a better exchange rate if you pay in dollars.
Often restaurants will have a dollar rate pasted inside the wallet that comes with the bill. If booking through your hotel just ask the person booking to find out if the restaurant has a dollar rate and what it is.
In Buenos Aires take a stroll down Florida and you will here the calls of "cambio, cambio" from numerous people offering to change money. The money is not always exchanged on the street but can be in an office inside one of the buildings.
The whole process is more open than people might realise and there is even a page on Twitter that gives the aproximate rate for the day Dolar Blue although don't necessarily expect to get this exact rate, probably it will be lower.