I did a quick google and this is what I found:
You need a PC gamepad. Any cheapass thing should suffice. Probably, the cheaper, the less weird technology it's got and the easier it is for you to use.
You take the 3DO controller apart and replace its innards with the PC gamepad's innards. Now just connect the 3DO controller's buttons to the same parts of its new innard where the similar-ish buttons used to be connected in the PC gamepad.
As a result you have:
1 piece of useless PC gamepad shells (just throw it away)
1 piece of useless 3DO controller innards (just throw them away)
1 working 3DO controller with PC gamepad innards in it. (don't throw this one away)
The theory is very easy, just solder solder tralalei. The only possible problem is that the PC gamepad's innards might not fit inside the 3DO gamepad. If that happens, then just saw off the end of the 3DO gamepad and let the innards stick out of it. It will look bad, but you will anyway be looking at the screen, not at the controller.
Apparently you don't have to know a heck of how the 3DO controller's pins actually go. Just make sure you check how the PC gamepad works before cutting all the cords.
Apparently a little school kid could get this kind of operation right
This information was found from the following websites:
http://www.gamesx.com/ (the left hand side menu has lots of interesting stuff in it)
http://groups.google.com/group/rec.games.video.3do/browse_thread/thread/545ffdb9c82a40d5/ff563a70d0e95f33?lnk=st&q=3do+controller#ff563a70d0e95f33For googling technical information
http://groups.google.com tends to yield far more usable results than
http://www.google.com/ .
Groups.google.com searches from the Newsgroups instead of the HTML Web.
Hopefully this was of any help. I am not an expert in this matter myself, I just repeated what I learned in the interesting twenty minutes I spent for this