My husband and I have hosted 5 exchange students (1 for 7mos and the rest for 10-11 mos each). It has been one of the greatest experiences we've ever had. It's been fun and challenging. We've learned more about ourselves and others than we ever expected. All except for our first student have been with Youth For Understanding (YFU). While not every student with YFU will be perfect for you family (or anyother for that matter), the students are screened and attend orientations to prepare for the experience. I can only speak from personal experience. (By the way, for the sake of confidentiality, I will use the words "her" and "she" even if the student was a boy.) The student that was with us for 7mos was with YFU. Our experience with her was not bad, but there was definitely a connection missing. I have also been an "Area Representative" and watched over a couple of families and students now. I had one student who had to change host families. The first host mother would not have minded if the student were sent 'back home'. Everytime I called the second host mom, she would say "she is such a delight" or "I love having her in my home" or something similar. My point here is that sometimes a student and family get matched and it ends up not being a good match. It's not the host family's "fault"; it's not the student's "fault"; it just wasn't meant to be.
With YFU, you do get to choose your student. The YFU staff and volunteers will try to assist you in to try to make sure it is a good match. Naturally, the selection of students is larger at the beginning of the 'placement cycle', and after school starts you may be limited to students who live in your school district that only have an "arrival family" (usually a family who wants to try out hosting before making a firm decision), but YFU will NEVER say "you must take this student". If it's at the end of the cycle, we may say "these are the only students left", but no one is forcing you to host.
Unless the student's native language is English, YFU students must take an English proficiency exam called the SLEP (Secondary Level English Proficiency) exam. Additionally, many schools require a particular minimum score on the SLEP. When a family is choosing a student, they will be given the students SLEP score and the number of years the student has studied English. Additionally, the student writes a letter (in English) to potential host families. (As a note, sometimes a student's English abilities get better after writing the letter and taking the test -- it may be a full 8 months between that time and the time they arrive.)
As far as sharing my experiences, that's hard - mostly because I have so many and Yahoo! Answers wouldn't let me put in everything I originally typed (it was too long). I can talk about the time I had to explain to our German son the difference between the meanings associated with the words "tall" and "long" (when talking about a male friend of mine). I can talk about how cool it was for our Latvian to get a letter in tennis even though she'd never played tennis before she got here. I can talk about how we were the shoulder to cry on when one of our students lost her great-grandmother and then grandmother. I can talk about how I often wonder how my grandfather (who passed away long before I was born) feel about the fact that he has a German great-grandson now even though it was his (my grandfather's) job in WWI to bomb German U-Boats. I can talk about how (with all but one of the kids) I counted the seconds until I could leave work everyday and go home to be with them. I can talk about how one host sister told me that she found that she was getting into fewer fights at school and with her parents after they started hosting a Japanese girl (i.e. she was learning to be more tolerant and patient). I can talk about how one host brother ran the slowest he had ever run during track regionals so that he could run right beside his German brother. I can talk about one host sister that grew to hate the student her family was hosting until the student went "back home" and then the host sister realized that she had totally screwed up an opportunity. I can talk about how we had to ground one of our girls and even though she'd never been grounded before, she is closer to me (in many ways) than with her natural mother. I can talk about how one host mom got a call from her Swiss daughter one day (after the daughter had gone back home) so that the girl could ask permission to go to a party (when the host mom said "you don't live here anymore, you don't have to ask me", the girl said "I know, but my parents don't care and I just felt like I should be asking".) I don't know where to start and where to end.
I hope all of this helps. Feel free to email me (DamEngineer@msn.com) if you want to ask more questions.