[emih]

Basically you get a bunch of problems (ranging from "check if a number is prime" to complicated graph theoretical problems) and some time to figure them out and code a correct & efficient solution. Often there are computer science concepts and reasoning techniques you need to know about (like biconnected components) to figure out how to make an efficient enough implementation.

The contests I used to go to, you got 11-13 problems and 5 hours to solve them with a team of 3. However, you only have one PC to share, so a lot of the time you are discussing, drawing stuff on paper and figuring out the solution in your head. There is also a printing service during the contest where you can literally get a paper version of your code :) so somebody else can code while you debug on paper.

See for instance https://www.acmicpc.net/category/detail/4319 for the kinds of problems they give (Korean website unfortunately but the problems are in English).