We have several links to help answer this question.
Read this post by a Mormon mom whose son just opened his mission call: Mormon Missionary Q&A
The CNN News Belief Blog just included a pretty good summary of Mormon missionary life while reporting about Elizabeth Smart’s other journey as a Mormon missionary in Europe. (Elizabeth Smart was kidnapped from her home when she was 14, and was found nine months later. She is on temporary leave from her mission for the trial of her abductor.)
How are mission calls issued? This talk from Elder Ronald Rasband about the importance of missionary service answers that question pretty clearly. He was invited to witness the process firsthand. He explains:
First, we knelt together in prayer….
As the process began, a picture of the missionary to be assigned would come up on one of the computer screens. As each picture appeared, to me it was as if the missionary were in the room with us. Elder Eyring would then greet the missionary with his kind and endearing voice: “Good morning, Elder Reier or Sister Yang. How are you today?”
“The MTC Experience” is a series of articles about what time in the Missionary Training Center in Provo, Utah, USA is like. (All missionaries attend a training center for s few weeks before they go to their assigned mission area.) The articles take you through the first day experience (see note below for clarification on one point), and include a list of services available in what was referred to as “Missionary Training City” (it’s a pretty self-contained campus — “made up of 19 buildings on approximately 30 acres of property.”). They also include information about other Missionary Training Centers in other parts of the world. (Read more about where these 16 other centers are in the “Missionary Training Centers” section of this web page.)
Editor’s Note: There is a difference now with the “first day” experience at the Provo MTC in that there isn’t a meeting with missionaries and their families anymore in the MTC — families now do a curbside dropoff instead.