What samsara is really about
If a newbie Buddhist asks how might a person free themselves from the cycle of birth and death there are several answers a modern Zen teacher might give. Perhaps one is that the cycle of birth and death is about reincarnation and since the Buddha doesn't believe in a soul that reincarnates, there are no cycles of birth and death. This is the last life. There are no others beyond itenjoy it while you can. But as any well read Buddhist can see, this answer is hogwash. It takes no account of the Buddha's real teaching.
First, it is necessary to grasp the real meaning of samsara. In a nutshell, to be in the condition of samsara means that one, as spirit (sattva), is trapped in the cycle of birth and death in which one is bound up with an uninterrupted succession of psychophysical (skandha) existences. One has never known otherwise than this condition.
Beings or sattvas according to the Buddha are unable to discern the most primordial (pubba koti), which is to say, they are unable to discern that which is free from samsara which is the primary substratum of all. Were, in fact, beings able to discern the most primordial they would realize that samsara heavily depends on beings seeing only a transitory image of reality, an image to which they automatically cling, going thus from one temporal body (skandha) to the next without interruption.
What the Buddha is really saying is that if beings connect with ultimate reality, from which all things are composed, they would automatically cease clinging to the delusion that things are unique and substantive. This would put an end to the cycle of birth and death. In addition, they would realize that things have never been other than illusory formations of the absolute substance which is Mind.