This video explains the algorithm of Delaunay triangulation nicely, even I could understand the concept.
First draw big triangle that contains all vertex, and draw circumcircle of triangle.
If some point (we call P) are inside of circumcircle of triangle (we call T), then that triangle should be removed, so we create new triangle by drawing several edges from P to the vertex of triangle T.
After, doing delaunay triangulation, we can conduct graph theoretic method such as calculation of minimum spanning tree based on the distance between two adjacent vertexs.