I want to understand the technicality of rebirth and what happens to conditioned self Correct me if I'm wrong about my current understanding of Buddhism: There is no eternal self or essence in me, but I am just a conditioned-self, an illusion created by the interaction of the five aggregates. Each time I do something, or will something, its this distorted conditioned-self in play, right?

Now, I want to understand what happens to this conditioned self when we die. You say its just an illusion, but lets take a practical example: A person dies in New York, and then is being reborn in Washington D.C the next moment. So here, you want to say the conditioned-self (illusion) travelled all the way from New York to D.C. to affect his/her next birth?

As a corollary to this question, I would also like to understand the technicality of kamma. Say a person violates the precept of non-killing in New York in his/her present birth. How does the kamma know whom to punish 50 years later when that same person is reborn in D.C.? (You may say here that there is no external law-maker, but kamma is just in our minds. But that's still begging the question - How does it know whom to punish 50 years later?)
The question of how karma works in light of the concept of non-self has been answered several times on this site (see "Related" in the sidebar). That being said, you raise a couple of interesting objections, namely the seemingly impossible jump through time and space.

First, let's be clear. The Buddha never said "there is no self". What he did say is that all things are non-self and that he didn't see any view of self that wouldn't lead to suffering for someone who held it.  This may sound like splitting hairs, but it is important in helping understand the nature of reality, as well as karma and rebirth.

Reality, according to the Buddha, is experience-based; this means that, to some extent, even time and space are dependent on the mind.  This is why body and mind (naama-ruupa) are said to be dependent on consciousness (vi~n~naa.na). Experience doesn't admit of things like "self" or "soul", or "cat" or "dog", for that matter. But it also doesn't admit of existential questions like "is there a self?" The question itself doesn't work in an experiential paradigm, since there is no impersonal spatio-temporal framework in which to place the object in question. "Is there a cat in the room?" requires the existence of a room to make sense.

In fact, experience doesn't admit of continuity, either, which is perhaps more pertinent to your question. The mind only lasts for a moment, being defined as the awareness of a single experience, arising and ceasing with the object of experience. Hearing this, it is common to question how rebirth and karma can therefore have any effect over space-time. Given, however, the premise that reality is based on experience, such questions are a matter of a conflation of paradigms.

Simply put, the mind doesn't move from one place to another, or last from one moment (or life) to another, "place" and "time" are considered a product of experience. An experience of seeing is "real" whether it occurs with eyes opened or closed. The idea that "I am in this room" is only valid in the context of the experiences that give rise to it.

I recently had an opportunity to watch a demo on Occulus Rift, my first experience of virtual reality. It's amazing how easily the mind is completely tricked into thinking that what it sees is "real". But that is the point; it is real, from within an experiential paradigm.

Scientists have done studies wherein they tricked a subject into thinking they were behind themselves, and the subject felt like they were outside their bodies. When sleeping, it is common for people to have out-of-body experiences. Near death, it is common to have OOBEs or or even visions of other worlds or deceased individuals. Some people claim to be visited by people who have recently died, or are on their death bed in far away cities. All of this is anecdotal, but it lends credence to the idea that the mind is at least somewhat independent of space, which from a Buddhist point of view is empirically true.

So, to actually answering your question, how does it work? The mind doesn't travel through space or time, space and time are a product of matter, which in turn is at least somewhat dependent on the mind ("Interdependent with" might be a better description). During life, body and mind work together to create the illusion of an impersonal spatio-temporal reality that is, in reality, made up of a causal framework (i.e. based on cause and effect) of momentary experiences that affect each other and direct one's life according to one's past deeds.

At the moment of death, something weird happens, but not categorically different. "The mind" has been habitually focussed on "the body", meaning that there is a habit for most experiences to occur in a specific locale, dependent on specific stimuli. The body, for all intents and purposes, is more like a prison than a progenitor for the mind. This is why OOBEs are uncommon and NDEs are actually fairly common (~20% by one doctor's estimation). Even still, the mind is capable of procuring visions of far away places and long-lost memories, especially when the body is dormant (i.e. dreaming when asleep).

At the moment of death, however, there is no pull of attraction to the body, so the mind is (mostly) free to wander. Strange things apparently happen after physical death, but eventually the mind states coalesce and decide upon a new object of attachment, usually based on old, engrained habits (humans become humans, etc.). As a result, and based on various karmic qualities, a new path is chosen and set out upon, giving rise to rebirth. This may lead the mind to appear to "travel" thousands or even millions or billions of kilometres in a moment, but what is really happening is that the new physical phenomena are being created by the mind, wherever the mind happens to incline. I.e., the newborn foetus's mind is affected by the prior mind of the being to be born, regardless of "where" that mind occurred. 

This concept of "movement" of the mind from one location to another actually occurs all the time; in human life, however, it is loosely limited to the confines of this six-foot frame. The point is, space-time is dependent on matter, not the other way around, and the mind is not entirely dependent on either (being able to remember past (and present) lives and even have visions of the future). This doesn't mean that the mind is entirely free to do as it chooses, it just means that it is confined to a different set of laws, ones that don't preclude the potential for it to arise in conjunction with physical phenomena in diverse reaches of the physical universe.

Interestingly, there are stories in the texts of rebirth-preparatory matter arising before one's mental relocation; mansions arising spontaneously in heaven to await their master who is busy doing good deeds on Earth, for example. This only presents difficulty if we are stuck in a spatio-temporal, impersonal paradigm for reality, which from a Buddhist point of view is absolutely false.

Karma is far more complex, but not difficult to understand in principle. The interactions between streams of conscious experience is causal as well, and leads beings to be reborn in connection with other beings who share their karmic histories, simply based on the energy of their past interactions, similar to the complex attractions and repulsions between physical particles. So, fifty years later, something you did in a past life might come back to kick you in the pants, just like a rock you throw away from the Earth can come back to hit you on the head. More importantly, everything we do at every moment has the potential to affect the immediate direction of the individual, meaning karma is very much about momentary causality, rather than future incidental results.

Sorry for the length, but I think this is actually a very important issue; what seems like a bit of tangential dilemma from a practical meditative point of view turns out to be a crucial sticking point towards proper understanding of reality and giving up views of self. Ultimately, however, you can only really understand these concepts by meditation on experiential reality; be reassured, however, that that is all it takes - no abstract ratiocination required :)