Electrolysis question, please help me, I have a test tomorrow!?

You have things mixed up. Sodium ions don't have their valence electrons because they've already lost them. That's why they are Na+. You might expect Na+ to gain an electron at the cathode and become sodium metal. That is what happens if you electrolyze molten sodium chloride. In an aqueous solution though, the reaction proceeds differently. The hydrogen in the water gains electrons more easily than sodium, so it's the hydrogen that gets reduced rather than the sodium. Thus, hydrogen gas is liberated at the cathode and chlorine gas at the anode.