Remember the meaning of congruent triangles. Two triangles are congruent if all 3 sides and 3 angles of one triangle equal all 3 sides and all 3 angles of the other triangle. CPCTC takes advantage of this fact. The general method is to first prove that 2 triangles are congruent and then use that knowledge to prove that a certain pair of corresponding sides or angles are congruent.
Consider the two triangles below.
If we want to prove that KJ = JI, we have to first prove that
HJK HJI . Once we know that the triangles are congruent, we can state that any pair of corresponding sides or angles are also, by definition of congruent triangles, congruent.
The proof below uses CPCTC to prove that the diagonals of a rhombus bisect the shape's angles. This proof relies upon CPCTC.
All that is necessary for this proof is the following definition for a rhombus: a parallelogram with four congruent sides.
HJK 
