how to solve the problems of wave motions

For solving the problems related to wave motion you have to keep in mind the property of waves, i.e., the basic equation of wave motion.
For other types of problems, i.e., in context of reflection and transmission, you have to mind the boundary conditions.
Related to resonance and standing waves you have to completely understand what is happening. In nutshell it is same as reflection and transmission as you have to obey the boundary conditions here also.