Some common phrases for expressing gratitude are "Thank you," "Thank you very much," "Thanks," "I owe you one," and "Thanks so much." These are all fairly common spoken ways of expressing gratitude in the English language.
It is also common to hear phrases such as "You're the best" and "Thanks a million" when someone is expressing gratitude for something. Some other common expressions are "I couldn't have done it without you," "You have no idea how much that means to me," and "You shouldn't have."
In formal writing, some common formal expressions for showing gratitude are "I would like to express my sincere gratitude" and "I am most grateful."