To connect an active subwoofer you would connect your sound card’s outputs to the inputs on the subwoofer, and then connect your full range speakers to the outputs of the subwoofer.
The subwoofer will handle the job of splitting the frequency range between the itself and the full range speakers using the crossover or adjustable low pass filter.
The typical signal flow looks like this:
Audio interface -> Subwoofer -> Full range speakers