Making phone calls in Uruguay

HI Maximilien
For landline, your only choice in ANTEL which is a state monopoly.
www.antel.com.uy
Once you have an address you go to one of their branches to make your request for landline.

Mobile phone operators are:
ANTEL (most common)
Movistar
Claro

Good Luck
Mikael

And what about cell phones? I understand you can buy one there just for Uruguay and you buy minutes to recharge it? What kind of cost is there?

You can buy a cheap cell phone from Antel or Moviestar for about $15.00 US and you can just add minutes each month for a few dollars.  You can do this at the checkout counter of any supermarket with Antel or go into Antel or Moviestar.

There may be other options as well.