What are prayers? To pray means to convey a request to God. Those who believe that there is no God can still pray to the higher power in who they have belief. But to say that there is no God, makes us feel very lonely at times. At times of crisis, who will you approach? Your friends might have left you. Your family might have deserted you. Who is left? There is God.
What is the first effect of prayer? The first effect is that we at least begin believing that someone who can help us, is listening to us. That gives a great support. Because you no longer feel very helpless or lonely. You have got a friend who is all powerful and who can help you. With prayer, we call for that help. The deeper the prayer, the earlier the help arrives. A prayer made in total faith can do wonders. But it all boils down to faith. And faith is a matter of individual belief. No science can comment about faith.
We send good wishes when someone falls sick or for someone who is facing tough times. How do prayers help in that situation? Here we are not making a selfish prayer, but asking for help for someone else. Collective prayers will surely reach God, and he will surely respond to them in his own way. His way may be different than our way, but respond he will. There is no doubt about that. This again is a matter of personal faith.
Imagine a man dying of cancer and family left with no hope. If every member of the family prays at that time, that member will also not feel very helpless and hope will always remain. Without prayers, all hope is lost. Wishing Good Luck, wishing for earlier recovery and inspiring a friend are all ways to connect with the higher power. Such wishes and prayers never go waste. Call God, and request him to help, the help will arrive if your prayer is made with faith and is heartfelt.