Read the question carefully, study the diagram provided and locate all the variables in the problem. These variables should include two masses (m and M, or a combination similar) and a distance (h). Acceleration is what you're looking for, but you may need to calculate/utilize velocity and work, as well.
Ask yourself how the system will move. According to Spark Notes SAT Test Preparation, "the heavy mass, M, will fall, lifting the smaller mass, m. Because the masses are connected, we know that the velocity of mass m is equal in magnitude to the velocity of mass M, but opposite in direction. Likewise, the acceleration of mass m is equal in magnitude to the acceleration of mass M, but opposite in direction."
Choose a coordinate system. Spark Notes mentions that some questions will provide one for you, but, if it doesn't, "choose one that will simplify your calculations. Follow the standard convention of saying that up is the positive y direction and down is the negative y direction."
Draw a free-body diagram. The pulley system will accelerate when released, so Spark Notes says that "we shouldn’t expect the net forces acting on the bodies in the system to be zero." An example of a free-body diagram is in the reference linked below.
Calculate acceleration. With two masses (M and m), two separate accelerations need to be calculated using the following equation:
a = (g(M-m))/(M+m)
Remember that g represents the acceleration due to gravity, a number which is a constant 9.8 m/s^2 in all equations.