My understanding of "no self"

My main question is this: If there is no "self" ("The "self" is itself a mental formation - a product of mind. It is therefore empty of inherent existence."), then what does Karma, or the result of our actions attach to? And further, what is reborn if not the self?
I know big questions. Can you answer them in 30 words or less? : )

Key to Buddhism is the idea of impermanence. Things are always changing. There is no self in the sense that there is no abiding (enduring) entity. Our karma attaches to that which is changing, and our karma (or actions) contributes to those changes.

Suzuki Roshi was one of the most important Zen teachers who brought Zen to America. He said,

"The teaching—the teaching that [laughter]—the teaching that everything is changing—in Japanese, shogyō-mujō[1]—or Chinese shogyō-mujō—teaching that everything is changing. This teaching can be—could be understand in two ways: the one—the teaching as the law of the truth. This teaching is always true, you know, whether we observe it or not. The—so—if everything is changing, that means non-substantiality. There is no substantial being, you know. We are only composed being from various elements. So we are non-substantial being. (a) Non-substantiality."

When I discuss my parents with my sisters we realize we each had different parents. Each of us constructed different parents, and our parents evolved and responded differently to each of us.

I like this description of rebirth from Wikopedia,

"Rebirth in Buddhism is the doctrine that the evolving consciousness (Pali: samvattanika-viññana)[1][2] or stream of consciousness (Pali: viññana-sotam,[3] Sanskrit: vijñāna-srotām, vijñāna-santāna, or citta-santāna) upon death (or "the dissolution of the aggregates" (P. khandhas, S. skandhas)), becomes one of the contributing causes for the arising of a new aggregation. The consciousness in the new person is neither identical nor entirely different from that in the deceased but the two form a causal continuum or stream."

Aggrevates are form, feeling, perception, mental formation or volition, and consciousness. It is the way that we experience the world.

The word "stream" is key in the quote above. One thing leads to another to another to another. 

Rebirth happens throughout our life, with each breath, with each time we walk into a room, with each day of our life. Zen people aren't very concerned with the rebirth at death, though a rare few say you are not a Buddhist if you don't "believe" in it. Even the Buddha said that we had enough to think about in this life (to reduce suffering). He was not interested in what happened next.

The real issue to me is how do we know things. Is it with the discursive mind, or is it the heart and intuition? You know that part of you that makes artistic decisions. "That's too close... that's too red... that's shape needs to be a little sharper." The difficulty in teaching art is that there is no way to really explain any of this. I was asked, "how do you know when to take a picture?" I had no idea how to answer that question. A famous violinist was asked how he did this very difficult movement. He could never do it again.

The most interesting thing about Zen for me is learning to understand without analyzing. Someone like Mr. Wikopedia could have all the right answers to your questions, yet would not really know anything in the same way that art historians do not know how to make a painting. As much as they know about the artistic process (much more than we do), they had no idea how to generate and develop an artistic idea.