I am not an expert on this subject so I may be wrong. So at the risk of Straight Doper style ridicule I will try to be helpful from my understanding of Buddhism (other religions may have different ideas). I write this in all sincerity.
Thus I have heard:
After you die, your consciousness goes into a limbo state called the Bardo by Tibetan Buddhists for (I think but I may be wrong) for 49 or maybe 50 days (I forgot) where you have no body to inhabit. Some Buddhists believe that one’s consciousness goes into another womb right away. Some other Buddhists said that both are true because the 49 or 50 days pass so quickly that it feels like a second because without a body your sense of time is altered, and you feel very disoriented during this Bardo phase. I have heard that one feels very lonely in this stage disconnected from everything.
I use the word consciousness because Buddhists don’t believe in a soul. I think Hindus believe in a soul called Atman. This is sort of a matter of semantics depending on how you define “soul”. If you think that the soul is permanent and never changing, then no, Buddhists don’t believe that. If you want to define soul as your consciousness that does change, then you could call it a soul.
So back to your question, I have heard that Buddhists believe your next body that you will inhabit is based on your karma from your last life and previous lives. Karma means “action”, meaning whatever patterns or habits that your consciousness has created. Your tendencies of action, personalities, thought patterns, etc will determine your next birth. In your next life, your tendencies will continue.
And it is not just in this world that you may be reborn. It could be anywhere, any universe. Yeah, weird, you could be reborn in a different dimension in a different universe. I heard this from my Buddhist teacher who is a Buddhist monk that I have know for two years. This explains earth’s population issue. You could be reborn as an animal or in heaven or hell. I think there are 6 realms (I am not sure about the 6, I am just a simple layperson). Actually I have heard human rebirths are very rare. Most likely you will be born an animal. You have wait more than a trillion lifetimes before you are reborn as a human. There is a common Buddhist allegory about the rarity of a human birth. That if there was a blind turtle swimming around the world’s oceans, and every once in a while that turtle went to the surface to take a breath of air. If there was a piece of wood with a knothole floating around the oceans, the chance of a human birth is about the chances of that turtle’s head going through the knothole of that wood. There is another metaphor a granite mountain that is a mile high and a mile long, and every (I think 100 or 1000 years or so) a bird flew over the mountain and one of its feathers brushed the top of the mountain. In the time it takes for the mountain to be worn away to nothing is how long you have to wait in between human births.
As for to end this cycle of rebirth which is called samsara, you have to realize absolute reality, in other words realize your enlightenment. I heard this takes a while. Then you get to be in nirvana (not the rock band).
Your karma is the reason you are reborn or caught in this cycle of samsara.
I have heard from my teacher that people do not realize their enlightenment is because of their misidentification. He said that he doesn’t like to use the word “attachment”, and another Buddhist teacher said “attachment” is a poor translation. (The same way dukkha is poorly translated into suffering.) They mistaken their body, thoughts, feelings, sensations, and memories as them when their true self is Buddha nature. In conventional reality, you are your body, thoughts, feelings, and sensations, but in absolute reality, that is not you. This misidentification is what keeps you from enlightenment and trapped in samsara. Once you realize your enlightenment, you will no longer suffer from karma.
As for remembering past lives, I have heard that is possible by intense meditation practice. My former teacher who is now in another country said that he did meditation practice using a huatou (sometimes spelled wato) for three months straight, and he remembered his past lives during a deep samadhi state.
I assume when you ask about governing agency, you were joking. That’s one of things I appreciate about Buddhism. You are in charge of your own salvation.
If you want to read more about it, I think the Tibetan Book of the Dead goes into this, and there are a lot of books on this subject.