How to calculate the rate constant of a zero order reaction?
According to your table, for a zero order reaction, you make a graph of the measured concentrations vs the corresponding times.  It will be a straight line, and the slope and intercept will give you the rate constant and the concentration at time zero.

For a first order reaction, you make a graph of the natural log of the concentrations vs the corresponding times.  It will be a straight line, and the slope and intercept will give you the rate constant and the concentration at time zero.