For my lab it says to draw all resonance structures of particular molecules, what does that mean?

It means draw all of the Lewis structures that make up the actual structure of the molecule. For example, to draw reesonance structures of benzene, draw two hexagons. In the first, put extra lines between the 12 o'clock and 1 o'clock positions, between 4 and 6, and between 8 and 10 o'clock. In the second, put the extra lines between the 2 and 4, the 6 and 8, and the 10 and 12 o'clock positions. The two structures are 1,3,5-cyclohexatriene and 2,4,6-cyclohexatriene. Resonance means that the real molecule averages together the classical structures drawn.

Not quite. Electrons in molecules able of resonance are not "fixed" in a particular structure, but instead alternate between different configurations, called resonance structures. The most common example is the benzene ring. It can be drawn as two different structures of six carbon rings with three alternate double bonds. None of these are the "true" configuration, they're rather both contributors to the net configuration, which is a probabillistic combination of both of them.

It means in that molecule some of the bonding electrons are shared by more than two atoms and you have to draw all of the possibilities out.  For example, O3 has two resonance structures:  O=O-O and O-O=O, so you have to draw them both.