One way in which an organic compound can be chiral is if it has an sp3-hybridized carbon that is a chirality center. Because of the tetrahedral geometry of sp3 carbons, there are two different ways to arrange four different groups in a tetrahedron.
A Carbon atom with 4 different groups attached will be a chirality center because of the tetrahedral geometry of sp3 hybridized carbon. Below are two versions of bromochlorofluoro methane, a 3-D view and a drawing. The carbon has four different atoms attached to it: Hydrogen, Fluorine, Chlorine and Bromine. Because of the tetrahedral geometry around the carbon atom, there are two ways to arrange these four atoms. The molecule on the right is the mirror image of the molecule on the right, but the two molecules are not superimposable: there is no way you can rotate one molecule so that all four atoms connected to the carbon will overlap on both molecules.
This holds true for larger molecules as well. If there is a carbon atom with four different groups attached to it, that carbon will be a chirality center.
Each of the starred carbons is a chirality center. The molecule on the bottom right is cholesterol, which has 8 chirality centers.