How does Buddhism explains rebirth and law of Karma? As per my readings on Buddhism it doesn't accept the notion of soul or Atman, but at the same time it accepts the law of Karma. 
How does Buddhism explains rebirth and law of Karma?
The Kamma can be understood as a seed in put in your mind, what goes to the next life according to Buddhism is the mind, not a soul, the mindstream does not stop when the body dies.

There is a great video on Kamma by Ven. Yuttadhammo Bhikkhu on youtube, I recommend you watch it, it is full of details and at the same time easy to understand, I will paste the link:

http://m.youtube.com/watch?v=ih0moT0bvgM