I found this to be particularly helpful:
What is the role of prayer? Can prayers be answered?There are many kinds of prayers. Some are designed to direct our minds toward a certain spiritual quality or aim, inspiring our mind to work to develop it and thus creating the cause for us to attain this. An example is praying to be more
tolerant and compassionate toward others. Other prayers are for specific people or situations, for example praying for a person's illness to be cured or for that person's mind to be peaceful and his life meaningful in spite of the illness.
For any prayer to be fulfilled, prayer alone isn't sufficient. The appropriate causes must also be created. We can't simply think, "Please, Buddha, make this and that happen. I'll relax and have tea while you do the work!" For example, if we pray to be more loving and compassionate and yet make no effort to control our anger, we aren't creating the cause for that prayer to be fulfilled. The transformation of our minds comes from our own effort, but we can pray for the Buddhas' inspiration to do so.
Receiving the blessings of the Buddhas doesn't mean that something tangible comes from the Buddha and goes into us. It means that our minds are transformed through the combined effort of the teachings, the guidance of the
Buddhas and bodhisattvas, and our own practice. "Requesting the Buddhas'blessings" has the connotation of requesting to be inspired by them so that our minds and actions are transformed and become more beneficial.
Some Buddhist practitioners seek to be born in a pure land in their next life because all the conditions there are conducive for Dharma practice and developing wisdom and compassion are comparatively easy. But we cannot pray to be born in a pure land and expect the Buddhas and bodhisattvas to
make it happen! We must also make effort to actualize the teachings by not selfishly clinging to worldly pleasures and by generating compassion and an understanding of emptiness. If we do our part, then praying will have a profound effect on our minds. On the other hand, if we make no attempt to
correct our harmful habits and if our minds are distracted while we pray, the effect is minimal.
Some people pray for another's sickness to be cured, for the family finances to improve, or for a deceased relative to have a good rebirth. For these things to occur, the other people involved must have created the necessary causes. If they have, our prayers provide the condition for the seed of constructive actions they did in the past to ripen into that result. However, if they haven't created the causal seeds through their own positive past actions, it's difficult for
our prayers to be fulfilled. We can put fertilizer and water on the ground, but if the farmer hasn't planted the seed, nothing will grow.
When the Buddha described the working of cause and effect in our mindstreams, he said that killing causes us to have short lives or much illness. Abandoning killing and saving the lives of others causes us to have a long life, free from illness. If we neglect to follow this basic advice and yet pray for a long
and healthy life, we have missed the point! On the other hand, if we abandon killing and save lives, prayers can help those positive seeds to ripen.
In addition, the Buddha said generosity is the cause of wealth. If we have been generous in a past life and now pray for our wealth to increase, our finances could improve. Yet, if we are miserly now, we are creating the cause for poverty,
not wealth, in the future. In this case, no matter how much we pray to be financially comfortable, our actions are creating the cause for the opposite result. Instead we need to cultivate generosity helping those in need and sharing what we have.
http://www.thubtenchodron.org/FAQ/faq.html 
