Not sure how to connect your PC-Engine/Famicom (hi, TapeDump users!) to your PC?  Well, you'll need a serial connection of some sort.  If you already have a serial port on your computer (RS-232), then you might want to use that, taking the precaution to convert the voltage with a MAX232 level converter, or take all the risk in keeping the RS-232 voltages the way they are.

Or, if you want something a bit safer, TTL (alias FTDI, alias UART, alias 5V serial) is becoming more popular these days since they are used to program Arduinos and the like.

Anyway, verify what you have:

RS-232 cable
(FTDI) TTL USB cable
(FTDI) TTL USB board

And note that I've written specialized versions of my program for either connection type, since the logic levels are different between them.  The following chart might give you a good idea of how serial data is represented with each cable/transmission type (RS-232 on top, TTL on bottom):