International Mathematics Olympiad is a highly respected competition which is held yearly. It is a place where many mathematicians are hoping to motivate the best students to continue their studies in Math. A lot of participants end up becoming the best mathematicians later in their career. My Ph.D. adviser Professor Gregory Margulis who won the Fields Medal in 1978- among many other prestigious Math prizes- won a silver medal in the 4th IMO. Two other examples of these mathematicians are 2006 and 2010 winners of Fields Medal, Terence Tao and Elon Lindenstrauss.
Different countries have different policies toward IMO. Some countries like China and my home country Iran train their teams for a long time, up to a year. Others may only hold a few exams and select their teams with a brief training.
This year the USA Math Olympiad exam is going to be held on April 27-28, 2011. As you might know, the exam is a 9 hour, 2 day exam with 3 questions each day. Generally, each day the 3 problems are sorted in the order of their difficulty. Meaning that you can generally expect the first and fourth problems to be the easiest problems. The third and sixth problems are usually the hardest ones. You can get more information about USAMO from their website here.
For more information about Math Olympiad Preparation, including some videos I made to help students, go here. If you'd like to sign-up for online tutoring with me, you can schedule a session with me here.