This is a map of the mission. It includes the shaded areas: the area north of Buenos Aires (in the top right in the box), and the southern part of the province of Santa Cruz, and all of the province of Tierra del Fuego (the southernmost part of the world other than Antarctica (named the 'Land of Fire' for the fires the people would build to keep themselves warm)). Click on it to see a larger version.
Now for a short description of how missions work. A missionary's purpose is to invite others to come unto Christ by helping them receive the restored gospel through faith in Jesus Christ and His atonement, repentance, baptism, receiving the gift of the Holy Ghost, and enduring to the end. A prospective missionary fills out some paperwork saying he/she wants to serve a mission and is physically capable. These papers are sent to church headquarters in Salt Lake City where one of the apostles decides where the missionary will serve. The missionary is sent a letter telling him where he will go and when to report.
The missionary reports to the Missionary Training Center (MTC), usually the one in Provo, Utah but there are ten or so more around the world. When the missionary reports he is assigned a companion and must always be with that person. Time in the MTC is spent learning the language and how to teach the gospel, the missionaries are pretty much in class all day. Usually missionaries spend two months in the MTC.
After the MTC, the missionary is put on a plane and sent to the mission offices. There he meets the mission president, a man who lives in the mission with his wife and children. The president is charge of the mission, including where each missionary will serve, who his companion will be, what schedule the missionaries will follow, etc. When the missionary arrives in the mission he is assigned a companion who will be his trainer. Every six weeks is transfers. At transfers the mission president decides if he wants to change where a missionary is serving or who his companion is. There are a few assistants to the president (APs). These assistants are regular missionaries who have been assigned to help the president in his administrative duties. Each mission is divided into zones. Each zone has a zone leader, a regular missionary who is assigned to be in charge of that zone. Each zone is divided into districts, and each district has a district leader.
The typical day for a missionary is as follows: wake up at 6:30, eat/shower/exercise until 8, study the scriptures until 9, study with companion and discuss plans for the day until 10, teach people until 9:30, get ready for bed and go to sleep at 10:30. "Teaching people" includes appointments that were made in advance to teach people, knocking on doors and talking to whoever answers (usually called tracting), talking to people on the street or buses. Hopefully people feed the missionaries food for lunch or dinner, if not they buy or make food themselves. One day a week is preparation day (p-day), where missionaries get to wash clothes, write letters, play sports, or go sight seeing.
Since missionaries completely devote their lives to God for two years there are many rules in place to help them focus on their purpose. These include: no internet access other than to write emails to family members, no tv or movies, no letter writing except on p-days, no calling home except twice a year (Christmas and Mothers' Day), no non-spiritual music, no books other than a few specific church books, no hugging members of the opposite gender, no swimming, and many more. These rules may seem strict but they are designed to keep the missionary's focus on the Lord and on the work he is there to do. As missionaries follow these rules God helps them to be effective in their efforts to bring souls to Him.