How do you find tension?(ropes and strings)

Tension of a rope is equal to the force applied to it. For example, if you tie a weight with a mass M to one end of a rope and hold it by the other end, then tension in the rope T = Mg.

FYI: Accelerating an object means applying a force to it. Please be more specific in your reply. Please also note that the question did not mention objects or accelerations, so you have to explicitly point to connections between tensions in strings/ropes and objects and their accelerations, if your goal is to clarify the matter.