What Buddhism says of Fate?
Fate in Buddhism, is but a wrong view. Our life and its event are not controlled by an external force (e.g. God, Heaven). All beings are bounded by their previous karma. We use another term call "Destiny" instead, to explain why some things which will happen to an individual will eventually happen. "Destiny", is the direct result of an individual's karma from his/her previous lives. The Karma (both wholesome and unwholesome) may be accumulated.
From a Buddhist perspective, a person's life and events is and will never be the result of a powerful God etc. A person is born into this world due to his previous Karma (both wholesome and unwholesome). In Buddhism, apart from Karma, the three poisons is also the primary causes of rebirth (Ignorance, Greed, Anger).
Events in life is also subjected to the uprisings and ceasations of many conditions, where without some conditions, things would not have happened in a particular way. For instance, you have planted some seeds of a certain plant (in this case Karma). However, without conditions like sunlight and water, your seed no matter how plentiful will not turn into a plant. When conditions do not arise, your seeds will remain as seeds until a period when conditions arise to enable to the seed to potentially grow.
It would be a mistake to blame an entity (e.g. a God) for all unfortunate events in a person's life. Many Theologist would argue saying bad things are not the fault of God but rather the work of a Devil etc, which sounds illogical to me. If God is so omnipotent, why would he like some people become so rich, while others tormented like slaves. If there was no past lives nor previous karma, how do you justify the difference in the lives of many people? (e.g. Broken families, Illness, Richness etc). Based on a probability game or a zero sum game?
As such, why can your destiny be predicted accurately through divination or fortune telling?
In China, the concept of "Destiny" (命运）is viewed as an important aspect of people's live. There is believe that whatever a person experiences is due to the person's own "Destiny". They believe that it is possible to know the outcome of a person's "Destiny" by calculating his/her birth character (生辰八字). This, although not recorded in Sutras, is supposedly a very accurate form of fortune telling.
Again, the day of your birth, your star signs, your location of birth is all the result of your own accumulated Karma from previous births. Why were you not born on 14 February 6pm but rather 17 February 5am for instance? Scientifically, birth of a child requires 9 months, but till date medical advancement can only predict the estimated date of birth. Even so, they cannot be certain of the date and time of birth. Nobody can explain why you were born on this date, only your Karma.
Thus, because of your Karma, you were born on a specific date and thus fortune tellers are able to calculate your birth character number or your horoscope signs etc. Your birth character number will determine many aspects of your lives, which is due to your past Karma but not the result of God/ Heaven. Some aspects of your life, like family you are born in and whether you are born with a silver spoon are not possible to change, but Destiny is not an irrevocable matter.
How can i change my Destiny?
One of the classics of Buddhist story for changing Destiny is here: http://www.buddhanet.net/pdf_file/liaofan.pdf
As all things in the world are subjected to impermanence, so is Destiny. You may been born a rich man's kid but if made the decision to squander your money away you may become poor. On the reverse, you may be born in a poor family but if you are diligent enough you can get a better profession when you grow up. However, your results are still subjected to conditions. For example, if you are born under the Caste systems in ancient time, it will be hard for social mobility to take place. But if through your merits you get a chance to leave the country, your life may be better. Thus, by accumulating better merits in your present life, if conditions still do not allow your life to change for the better, do not despair as you are still making a better path for yourself in your future lives.
On the side note, I am no expert in such matters but just sharing my knowledge of what i know of the concept of Fate in Buddhism. Should you have any queries or feel like having a discussion, feel free to comment on my post. Thanks!