The group leader takes a number of straws or similar long cylindrical objects, and makes sure one of them is physically shorter than the rest. He then grabs all the straws in his fist such that all of them appear to be of the same length.
The leader then offers the clenched fist to the group. Each member of the group draws a straw from the fist. At the end of the offering, the person with the shortest straw is the one who has to do the task.
This practice is immortalized in the cliché "drawing the short straw," meaning to be randomly, unluckily, or unfairly selected to perform a task or suffer some penalty.