Subwoofers are used in most home theater systems, but subs can also radically improve the sound of stereo systems -- and not just the ones with small speakers. Subs can provide a foundation to the sound that few speakers can muster on their own. So adding a sub is not just about adding more and deeper bass; rather, a properly integrated subwoofer can improve the overall sound of the system.
Subwoofer connection to a two-channel system differs from the methods used in home theaters. AV receivers feature bass management to direct the low bass frequencies to the sub and the midrange and treble frequencies to the speakers. The subwoofer is hooked up to the receiver with a single interconnect cable.
Stereo receivers, pre-amps, and integrated amplifiers rarely have subwoofer output jacks or offer bass-management options. So instead of using those connections, we'll use the subwoofer's speaker-level, aka "high-level," inputs. Most, but not all, subwoofers have these inputs; they get connected using speaker cables to the same speaker output jacks on your receiver or amplifier that are also hooked up to your speakers. That means you have to double up the connections on the receiver or amplifier (see photo below that illustrates that connection method).
With this arrangement, the stereo speakers and sub receive all of the bass, midrange, and treble frequencies. The sub will use its built-in crossover (aka "low pass" filter) to determine the upper limit of the frequencies produced by the subwoofer. With small speakers with 4-inch or smaller woofers, you'll set the sub's crossover frequency at 100Hz or higher, and with speakers with 5-inch or larger woofers, 80Hz or lower. Then set the sub's volume control to provide the level of bass support you want. I like to bring the sub's volume up to the point where I just start to hear the bass filling out the speakers' sound, but some listeners prefer more pronounced bass fullness. I usually spend at least a few hours listening with lots of different types of music to fine-tune the crossover and subwoofer volume settings.
For more information read this post on how to set up a subwoofer.