There are two main phone companies for landline service in Buenos Aires:
For any apartments rented from an agency, a landline with service (and usually voicemail) will be included in your monthly rent and will already be set up and working when you move in. If you are moving in to an unfurnished apartment or home, you will need to contact these companies directly to begin setup of service. The prices vary on what kind of a plan you want, but generally start around AR$45 per month. It is very common that the basic service will not allow you to make long-distance or international calls, or even call cell phones. So be sure to stipulate if you want these services.
You can order these services online if you can navigate the Spanish content. It is uncommon to get a customer service representative on the phone who speaks English, and there aren't English divisions. If you don't speak Spanish, many expats suggest asking the person who helped you locate your house or apartment, or your landlord, to help you with this process, and most are more than willing to lend a helping hand. You will find with phone installation, as with most things in Buenos Aires, that relying on an estimated delivery date is unwise. Be prepared to wait several days for a technician to come to install the line, and be prepared for them to be unapologetic if they are later than estimated.