Check out "The Phasing Method of SSB Generation" on
http://members.tripod.com/michaelgellis/mixerscom.html
It has a diagram of how I was explaining to generate SSB. The diagram
has the math for the signals, so you can see how the SSB is eventually
generated by generating two DSB signals, then cancelling one of the
sideband by summing or subtracting the signals.

I'm going to let it slide, but I really don't like those comments about
SSB being AM if you blah blah blah. They are true, but I don't believe
they are useful in comprehending the modulation scheme. It is better to
think of SSB, well at least USB, as just the voice signal (baseband
audio) shifted up to a radio frequency. [If the voice signal was a 1Khz
tone and the carrier was 10Mhz, then there would be a signal at
10Mhz+1Khz. It's that simple.] When you demodulate USB, you basically
shift it back down to audio with a mixer. If you don't shift it
correctly, you get the Donald Duck sound since the frequencies are
offset a bit. LSB is slightly different in that the audio spectrum is
reversed, much like that cheap frequency inversion used in "secure"
communications.