I believe intonation is something one becomes familiar with only after learning the language for quite a while. Without substantial background knowledge, it is hard to pick up the intonation. (I know this is not much help, but I wanted to register one answer so that people don't constantly open it up thinking there was no response at all :)

I agree. The only way to know how it sounds is to listen! Also, mimic/shadow! That will give you a general feel and work on some basics. But since intonation is associated with meaning, knowing what you're saying will help you understand. The grammar has a lot of nuances too. You'll get it! Korean is more monotonous compared to American English/valley speak/etc. Depends on what you're saying. Certain little words and sound effects will sound more emotional.

The best suggestion would be listening and watching Korean movies and TV shows. If you watch a Korean person speak, they move their mouths differently when they want to put more emphasis, say something cute etc. If you mimic how they speak that would be helpful. Then listen to them, close your eyes and listen to where the 'stress' points are. I find, generally, Korean people pause with grammar points (just my observation); when they use ~고, ~는데, ~지만, ~잖아 This when I commonly hear it. You want to listen to the 'rhythm' of the language. Hope this helps