/Does the law of karma apply to everybody?/
The law of karma applies to everyone and at the same time one can transcend it by one's meditation. The law of karma exists and at the same time it can be transcended by realization, oneness with God and by the power of spirituality.
/Could you please explain how the law of karma affects us in this life and our next life?/
We are carrying the past inside us. It is a continuous flow. "As you sow, so you reap." If we do something wrong, we have to know that either today or tomorrow, either in the physical world or in the inner world, we will get the result. If I constantly steal, one day I will be caught and put into jail. I may not get caught today, but one day I will be caught. And if I do something good, if I pray, if I meditate and do divine things, I will get the result of this also. Sometimes we see someone who has done something wrong enjoying the world. But perhaps he did something extraordinary, something wonderful in his immediate past incarnation, and now he is having the result of his good action, while the results of his bad deeds have not yet started to bear fruit. In the evening of his life, or in a future life, he will definitely be punished.
In the case of an ordinary, unaspiring person, karmic dispensation is unavoidable, inevitable. The law of karma is always binding; like a snake it will coil around him. He has to pay the toll, the tax; the law of karma is merciless. But again, there is something called divine grace. Suppose I was ignorant and I did a few things wrong. If I shed bitter tears and cry for forgiveness, then naturally God's compassion will dawn on me. When a person enters into the spiritual life, his karma can easily be nullified if it is the Will of God operating through a spiritual Master. Slowly God's infinite grace can nullify the results of his bad karma and expedite the results of his good karma.