By boat, or more specifically, ferry. This is why North Korea gets angry whenever Japan decides to sanction the ferry route between the two countries. Though I guess they haven't let that route run since 2006, I'm not sure how they do it now.
Japan doesnt have normalized relations with NK. You can't just take a boat there with bags full of yen.
I think what you've heard is probably a reflection of SOUTH Koreans who work in Japan, who are discriminated against by the Japanese, and as such work in places like pachinko parlors because bigotry keeps them out of more reputable and better paying jobs. They do ship money back to family in SK.
Northern Koreans are trapped by their regime and escapees are rare.
The bigotry towards South Koreans in Japan and how so many of them are forced to work in pachinko or other shady businesses is so common there's even a famous novel about it:
