One very useful tool for finding period changes is to compute what is called "O-C" ("O minus C") diagrams. It is based on the following idea: if a star is perfectly periodic, then every period is exactly the same. In that case, we can predict its cycles in advance. If one minimum occurs on, say JD 2450000, and the period is precisely 332 days (and never changes!), then the next minimum will occur on JD 2450332. Then we can compare our predictions with future observations. By observing the star, we can calculate the observed time of minimum and compare it with our predicted time of minimum by simply taking the difference between the observed and computed times of minimum. These are the "O-C" or "observed minus computed" values. After you have determined the O-C values, you can plot O-C as a function of cycle number.
When the O-C values lie on a straight line which is horizontal, the system is periodic and agrees with the calculated value of the period. If the O-C values lie on a straight line that is not horizontal, the system is periodic but the estimated period is not correct and the slope of this line is the difference between the true and estimated periods. When the O-C values change from one straight line to another which has a different slope, the period has changed and the slope of each line is the difference between its period and the estimated period. Finally, when the O-C values do not follow a straight line, the system is not perfectly periodic.