If you don't see a row of sockets with 1/8 inch holes like these four, you will need to have a soundcard installed!
The back of a computer showing a soundcard

This is a Sound Blaster® soundcard.
The cord from the speaker is going to be be plugged into the black output socket.
There are often two different outputs, one labeled "Speaker out" and the other "Line out". The first one is usually better for speakers and the other for a home stereo. The microphone jack is often labeled "Mic In".