Connecting the positive side from the receiver to the negative post on the speaker and vice/versa. This usually results in poor sound from your speakers and can damage them, basically the cones in the speaker are moving in the wrong direction, or out of phase.
No, that's not the case at all. Wiring things out of phase will damage nothing.
However, all your speakers should remain in phase together. The easiest way to illustrate what out of phase speakers do is to properly setup your L/R speakers and sit in the sweetspot so they are exactly the same distance from you. Now reverse the wiring on one. What occurs is that when the drivers in one speaker are moving outwards, the drivers in the other are out of phase and moving inwards. This can cancel out low bass, but it also causes problems with imaging especially center-imaging which is created by both speakers playing the same sound equally. Play white or pink noise with your speakers in phase and it will image very strongly in the center, out of phase it will sound like it's coming more from the sides or behind you. There are phase-check tests which do this on test discs like Avia which also may be interesting.
Point is you want to wire things in phase, but nothing will get damaged at all.