Best way to modify broken headphones cables to arduino-able cables

Hello, so I noticed the other day i Had a lot of broken headphones, that only output sound from one earbud.

Trying to reclycle them, I cut them, and stripped the cable, exposing the two conectors, it is the wild hair type of cable: I managed to test them with the arduino, but conecting them to the protoboard was a nightmare, and I don't know if anybody knows a way to make them more "arduino-able" or "protoboard-able" to conect them more easily.

Thanks in advance and excuse any spelling errors.