Connect a crossover device in between your mixer and subwoofer amplifier. Connect two XLR cables to your mixer's main output jacks and the other ends into your crossover's left and right inputs. The crossover divides the incoming audio signal into two separate halves (low/mid-hi), so that each type of speaker in your PA system will be sent the type of range they support.
Adjust the crossover's frequency setting to match the lowest frequencies your passive PA speakers support. Most PA speakers used for left and right channels cut off frequencies within the 50 to 60Hz range. Setting your crossover's frequency at this value will send all frequencies below the determined setting to the subwoofer instead.
Connect the crossover to your amplifiers. Plug an end of a pair of XLR cables into the crossover's high channel output jacks, and then plug the other ends into your high/mid amplifier's left and right XLR inputs. Plug another XLR cable into your crossover's mono low output jack and the other end into your subwoofer amplifier's XLR mono input jack.
Connect your speakers and subwoofer to the amplifiers. Plug an end of a pair of speakon cables into the left and right main outputs on the amplifier, and then into the left and right passive PA speakers. Plug another XLR cable into your subwoofer amplifier's mono output, and then into your subwoofer's XLR input jack.
Test your subwoofer by playing a sub synth tone on your synthesizer keyboard. Plug one end of a quarter-inch instrument cable into your keyboard's main mono output, and then into a channel on your mixer. Select a sine wave tone and play various notes in the lower octaves. Listen to your subwoofer's performance while playing short notes and those with sustain as well. The transients of the keyboard can be used more effectively than those that are already compressed on professional studio recordings.
Adjust the mixer's master low EQ to correct any muddiness. Set the cutoff on the EQ at 30Hz, for frequencies under that are unable to be heard by the human ear and create rumble. Your audience will feel the extreme lows within your mix in the 30 to 40Hz range, which is, in most cases, the lowest frequency output your subwoofer can produce. Above these low frequencies is where human ear start distinguishing lows from mids and highs.