Yes. I have had so many prayers answered. In fact, my whole life today is an answer to prayers. I prayed for things and God gave me all the things I had asked for, in ways more surprising and beautiful and perfect then I ever could have imagined or hoped for myself.
I have also experienced absolute miracles including a man rushed to hospital and not expected to survive, and after he was prayed for by our church group the doctor was astonished to find that he had made a full recovery - not only would he live, but when he woke up, symptoms that he should have (by every understanding of medicine) had to live with, had totally gone.
Miracles DO happen. Pray and believe.
Do you go to church? As it is also really healing and helpful to have other people pray for you too. When I feel especially weak or worried I ask other Christians to pray for me, it provides no end of comfort and also I firmly believe that prayers are answered. Whenever they're NOT, it's because God is protecting us from something, or because God has an even better plan for us that couldn't come together if He answers our prayer for the thing we want at this moment.
So I also have a number of things that I prayed for but didn't happen, and at the time I was unhappy or confused about why, but when I look back on now, I'm SO overwhelmed with gratitude and happiness that the specific prayer wasn't answered because if it had been, I wouldn't have been led to this much better thing. God never abandons us, it's just that sometimes we don't understand at that moment what He's doing.
(When I say 'pray', I'm referring to praying to the Christian God, and as a Christian I obviously don't believe that prayers offered to other gods or 'the universe' are effective. In fact, the very opposite.)
There is no specific way to have to pray. No certain words you need to say. Just talk to God. Even just talk to Him as you'd talk to a friend or a family member! God loves you and wants a relationship with you. Obviously love isn't forceful, and love isn't controlling, so God won't force Himself on you, but He ALWAYS desires a relationship with you, He is ALWAYS there waiting for you to come back to Him, He is ALWAYS listening.