You could say: Thank you so much! I really appreciate that!

It depends on your relationship with that person. If it is a friend or someone that is of the same level as you, you can say "Thanks! I owe you one." Or for example if someone gives you something you didn't ask for but you appreciate the thought, you can say "You really shouldn't have." These are all informal. Formal ways or extreme ways of thanking someone are "I am very grateful for...(insert thing you are grateful for)." Or you can say "I really appreciate...(insert thing you appreciate them for)." Another way of formally thanking someone is to say "I am much obliged". being obliged is the feeling of being indebted to someone. But it's very formal and I might never say this word. The most safe way formal/or informal is "Thank you so much." "Thank you very much." or Thank you SO much" emphasis on the "so" or "very"

You'd say , "Thank you very much!" How to express, as in an action, maybe shake their hand if you don't know them very well. Maybe give them a hug if you are well acquainted. Hope I answered your question...