This project was pulled straight from a second year Electrical Engineering lab session (to which I was not privy). The whole concept is based around using differential amplifier. Although I can no longer find the document that I followed to make this project a very similar one can be found here on Instructables. The point of this differential amplifier is to "amplify the signal we're interested in (muscle activity) without increasing the noise (often from external electrical interference)"[Article Step 2].
After constructing this circuit I programmed an arduino to filter the output and detect if the signal had crossed over a reasonable threshold. This threshold was found by experimentation, I don't love this method but it was easy. If I had been so inclined, maybe a dynamic threshold or even a trainer function linked to a button press would have been more elegant. Anyhoo, at the Hackspace I hooked up a broken NES controller PCB to the output of the arduino such that if that threshold was crossed a button press would be simulated. We ended up connecting three EMG electrodes, one my left and right biceps and right pectoral muscles respectively, and were able to quote on quote, play, "Super Mario Bros" with relative success.