When NEC created the PC Engine they weren't thinking about global domination. In fact, given their half-assed efforts in the US and Europe, they never really did give it serious thought. This means the 'protection' in their system is sort of weak, but also annoyingly two-phased.
The theory: The HuCard pinout is identical for US and JP games, except for the 8 data lines which are reversed (0-7 becomes 7-0). This is a simple matter for an adaptor to fix, but there's one additional wrinkle: you need to set the region on Japanese consoles before American games will work, the adaptor alone is not enough. The reverse is not the case: Japanese games don't check the system region, so they'll run fine on US systems with an adaptor.
So, if you have an adaptor and Japanese console, you need to mod the system before it'll work. If you have an adaptor and American system, you're done, go play.
The fix: On Japanese systems, connect pin 29 of the Hu6280 chip to GND. That's it.
This mod is dead easy to perform. The most difficult part is opening the unit. The Japanese Duo-R uses security-torx bits, and most other units (CoreGrafx, PCE, SuperGrafx) use GameBit screws. Once that's accomplished, simply look for the chip labelled Hu6280.
On the board are some white labels, indicating the pin numbers. Now locate pin 29 of this chip, and now comes the tricky bit.
Take a soldering iron and heat the base of pin 29, while gently prying up at it with a small jewelers screwdriver or x-acto knife. You want to lift it off the board so that it sticks straight out.
Now, connect this pin to GND with a wire. GND is easy to find, any metal shielding will be ground, all connectors will have at least one grounded pin, etc.