This isn't for everybody. If you want to receive pirate broadcasts as quickly and easily as possible, bite the bullet and shell out the extra bucks for a receiver that has SSB capability.
If, however, you want to learn a little about how SSB works, or you absolutely cannot afford a more sophisticated shortwave receiver, try the following.
Get a second radio that picks up the AM broadcast band, or another inexpensive shortwave. You will need an older one; the newer, digital ones don't work as well. Put the second radio as close physically as you can to the shortwave receiver. Put the shortwave on the frequency you want to receive. Now tune the second radio back and forth. You are listening for a whistling noise which makes a blip on the shortwave as you tune across. When you hear it, tune the blip as slowly as possible back and forth across the SSB signal you are trying to receive. You will hear the SSB signal suddenly become clearer. It will vary in pitch as you tune the blip back and forth. Listen carefully and you will find a spot where the blip makes the SSB signal perfectly readable. Changing the tuning on the shortwave or the second receiver will change the pitch of the received signal.
This is all pretty inexact. You will have to experiment with positioning. If the blip is weak, try wrapping a couple of turns of wire around the second receiver and attaching this wire to the antenna input, along with your regular antenna. If the first radio you try doesn't work, try another. If you can possibly find one, an old tube-type radio works best.
The theory behind this whole thing is that the local oscillator in the second receiver, which makes a radio signal of its own, supplies the missing carrier and sideband by heterodyning action. Local oscillators are not very stable, and you will have to continuously retune the second radio to keep the received signal at the correct pitch. Or you could just go out and buy a Yacht Boy.