How can we find the direction of acceleration in pulley systems so that we can write equation of motion for different parts of the pulley system. Do we have to assume acceleration in some particular direction?
Yes, it depends upon the force, that resultant force acts in which direction like, take this example If pulley is hanging from a rigid support say roof and masses are connected as shown in figure given below.
(assumption: block m2 is heavy then M)
Fbd becomes now as you seen in diagram, how the resultant force shows the direction of acceleration of body.