The 2 major requirements that are unique to international students are:
Language proficiency is usually demonstrated by the TOEFL, although MELAB or IELTS scores can be substituted. The School of Statistics generally requires at least 600 (paper based) or 250 (computer based) or 100 (internet based) on the TOEFL for admission to the PhD program or to work as a TA; the 600/250/100 scores are considered to be roughly comparable. Corresponding minima are 80 on MELAB and 6.5 on IELTS.
If you have completed 16 semester credits (within the past 24 months) in an academic program in a recognized institution of higher learning in the U.S., you do not need to submit the TOEFL as part of the application. You should note in your application materials that you are exempt from TOEFL for that reason.
By Minnesota State law, teaching assistants for whom English is a second language and who have not studied previously in the United States must pass a spoken English test, the SPEAK test, given by the University of Minnesota. If you do not pass the exam, you are required to take a remedial course in English. It is expected that all students who receive a teaching assistantship will have passed this exam by the end of their first year of graduate study.
The visa process has become more burdensome since the terrorist attacks of September 11, 2001. In particular, there are new or increased fees for various immigration steps, nearly every applicant is now required to have a personal interview at a US consulate, and there can be substantial delays along the way. The International Students and Scholars Service at the University of Minnesota has considerable useful information about obtaining the visa.
Here is a rough description of the steps.