I have done my research and watched the videos on how to re-light the pilot light on my water heater but nothing happens. It does not relight and then go back out. It's just won't relight at all. I know I am following the directions correctly and my dad has even tried to walk me through it over the phone. What am I doing wrong?

Fyi - pilot light was lit when we left for the weekend - we came back 3 days later to not hot water and the pilot light out.

Your thermocouple is the likley culprit. Replace it.

First, make sure you follow lighting instruction. Then do as Ballenberg1 said...