For example, I know Russia never wanted to give China nuclear tech during the Cold War, what was preventing them from finding it online and engineering through there?

Well, the internet as you know it did not generally exist during the Cold War, so, it was a bit more complicated than "going online" and looking it up. The internet really didn't become the internet until the late 90s/early 2000s and the Cold War ended in 1991.

And countries like N. Korea, why is it so hard (until recently) to build a stable nuclear weapon?

Building the physics package (the part that goes boom) of a nuclear weapon is easy. That's generally the sort of information that you find on the internet. Essentially, in its most basic form, it's just shaped charges that compress two half spheres of uranium 235.

The hard part is finding the Uranium 235. Remember a couple of years ago, how someone hacked a bunch of Iranian centrifuges with the Stuxnet virus? Those centrifuges are the important part of making a nuclear weapon because they enable the separation of the Uranium 235 from the rest of the Uranium. U-235 is what makes the boom in the bomb.

There's also plutonium weapons, but once again, the difficulty is in refining the plutonium in order to make it go boom.

In the US, the effort to develop a nuclear bomb was called the Manhattan project. For a good idea of the practical difficulties of making a nuclear bomb, I'd recommend reading about that. http://www.atomicarchive.com/History/mp/