From what I understand, the loudspeakers I currently use carry highs and mids.
Not exactly. Those speakers, like most "top" cabinets in a PA, can reproduce the full range of human hearing (or try to). The weak part is in reproducing the extreme low frequencies, hence a subwoofer is usually added. By high-passing the tops (cutting off the extreme lows), they are able to perform a better job on the remaining frequencies, leaving the subs to do the extreme LF. This is where a crossover is most helpful. It not only high-passes the frequencies to the tops but also low-passes the frequencies to the subwoofer.
If you only have a two-channel amplifier and want to use one channel for the sub(s), then you will have to make a choice for the tops. Do you want to run just the left or right channel, thereby losing stereo information (there is usually not much of it)? Or do you want to combine the left and right signals to mono and then send that to the remaining amp channel. Either way you will not have a stereo image. Personally, I would recommend mixing to mono; at least you will be reproducing all of the music (do a forum search for methods of doing this). When you get a few bucks together, buy a second amplifier and use one amplifier (even if only one channel) for the sub and the other amplifier for L-R stereo for the tops.
Note: DO NOT use a Y-cable to combine left and right outputs to get a mono mix. That is the wrong way to do it.