The families of the missionaries pay a monthly stipend (I believe it is currently $400'ish) per month. This covers their food, housing and transportation during the course of their mission. Since some places cost more and some cost less, everything averages out.
They also go through orientation/training, and are evaluated where they would best be of service - languages spoken/understood, health, etc. (I believe) are all considered. (Spanish speaking has sent a lot of young missionaries to the south-east Michigan area!) They rotate through several different roles and multiple locations during the 22 months (on average), and are only allowed to "phone home" (although writing letters is encouraged) a few times a year. They also don't watch television or read anything except scripture during that time, as they are strictly concentrating on service to others and their faith.
ON EDIT: The rules are ones they follow *for themselves*; there are no "missionary police" making them do this, but the rules are clearly understood when they sign up. Also, they can quit anytime, with no questions asked. END EDIT
It isn't easy for them, but it does give them an excellent ability to speak clearly about what is important to them, face rejection with calm acceptance, and still show respect for others, even when they aren't being respected themselves.
I have always been impressed by the young missionaries we have been acquainted with; taking two years out of your life in service to your faith and others is something I admire.
Also, while they are very picky about even giving the "appearance" of impropriety - (ex: male missionaries will not be alone in a house with a woman without some form of chaperonage to protect against charges of misconduct by anyone), they are always willing to "provide service" to those who request it. This means they will gladly rake leaves/shovel side walks for seniors (even not of their faith), make sure appropriate people are notified if someone requires food/clothing assistance, and pretty much anything else reasonable you could ask of them.
Disclosure: We have been feeding young missionaries for 20 years. 
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