A fire-wire or USB2 connection is really all that you need.
What Chainzsaw is suggesting is to playback your analog Hi8s and 'capture' the stream through a computer TV tuner installed in an internal slot. This will certainly work but you would be limited to the tuner capture format and resolution.
I would suggest investigating the native output format, resolution and bit rate of your Hi8 recorder. Then find some software (and subsequently, hardware) that will capture it natively at the same output format, resolution and bit rate without any compression or conversion.
Hi8 analog tapes are of decent video quality -- near production-quality type of stuff (especially when shot at SP). You need to guard against any degradation or conversion of this quality. At least at first. Once you have the original native video captured digitally, you can go crazy on some movies and still revert to the saved original if you go too far.
What camera did you use? Do you know its native formats? I suspect it's a decent standard definition Hi8 that when taken digital (correctly ) can make some great movies.
If it was a Sony you should probably check out Vegas Studio.
Not sure if you are still the movie master, but most any new HD recorder will function as a capture device for you.