As a student, especially an exchange student it is probably of no interest to rent an apartment through a real estate agency as contracts are of a minimum of two years. But there are other options.
The first option is the housing program of your university. Many Argentinean universities offer help to find a place to live. Housing ranges from placing you in a family, living in university apartments or offering independent housing. If you decide independent living is what you want, you might consider looking around at your Argentinean university’s notice boards as well as on notice boards at other universities. Also contact the exchange coordinator of the university you will study at and ask for the contact information of exchange students that are already studying at the host university. Many rooms are advertised by word of mouth and students that already spend some time at the host university will know what is available. A good tip is to ask at your home university for students that will be finished their studies in Argentina.
A second option is to stay at a Residencia. Residencias generally offer private, double and 3 or 4 person rooms which can be rented for longer periods. Both Argentinean and foreign students make use of them. Home-stays are private owned apartments where the owners rent out one or more rooms. Although home-stays tend to aim at short-term visitors, some of them are willing to take in students for a semester in which case you can negotiate the price.
There are also various student housing agencies in the mayor Argentinean student cities. Ask your host university for recommendations. In general you will have to pay these agencies to get a list of available rooms and apartments. Next it is up to you to contact the owners and make appointments. If you find a place you like, a contract is drawn and commission has to be paid to the housing agency. This commission is normally one month of rent.
When looking for student accommodation you will notice that certain neighbourhoods are more popular among students than others. Moving away just a little can result in good deals on housing. However, check how the public transport connection with the university is. You will most likely be travelling at peak hours in the morning so a good connection might save you a lot of time and good humour.
You can also post messages and read the Housing Classifieds and Forum at Just Landed.