I'm from Taiwan and have some experiences on IOI[1] and ACM-ICPC (but never enter National representative or ICPC world final). We also spend many times on training. IOI is country-level contest, so every country has its own tournaments to find out top-level students as their National representative, like: USACO[2].

Usually Many of us start to know these kind of contest by IOI at high school (16 years old), while some geniuses may learn even younger.

First we need to learn C/C++/Java, algorithms, data structure and so on ( For example,Read the book "introduction to algorithms" at that age), then learn how to solve problems on that contest by UVa Online Judge[3], TopCoder and so on. So it's a long road from high school to university, but solving problems is sometimes interesting.

[1] http://www.ioinformatics.org/history.shtml [2] http://www.usaco.org/ [3] http://uva.onlinejudge.org/