An algorithm is a step-by-step list of instructions for doing something. Most people know an algorithm for tying their shoes. Mathematicians like to create algorithms for doing mathematical things.
Your next task is to create an algorithm for coloring any graph. As you do this, it may be useful to consider vertices according to how many edges are touching it. This is called the degree of the vertex.
When you think you are done, try your algorithm on the graph below. You should find that this graph has a chromatic number of 4.