How will you select a small group from a large one?

Very often we face the problem of selection a few persons fro a group. If certain specifications are given it is easy, I mean if the condition specifies that the selected persons must be sports men or they must be musicians like that.But if there are no such restrictions, only condition is that it must be a representative sample of the large group. Then how can such a sample group can be chosen ?

This selection may be, sometimes, for knowing the general characteristics of the larger group. May be to know the skill of all students in a particular class in solving mathematical problems.