It's pretty simple, but I'm having a hard time explaining it simply.

Let's take an example:
Tomorrow night (Thursday), Pittsburgh is playing at home against Tennessee. The spread is Pittburgh being favored to win by 6 points. That means that the imaginary banana in the sky thinks it is equally likely that the Steelers will win by more than 6 points as it is that they will win by less than 6 points or lose.
So, when filling out your picks, you decide to yourself, do you think the Steelers will win by more than 6? If yes, then you select them. If you think the Titans will win, you select them. And if you think the Steelers will win, but not by 6 points, then you also select the Titans in your list.
Basically, I go through the list, and if I think the underdog will win, I pick them right then. For the rest of the games when I think the favorite will win, I look at the spread (use the one marked Final in the list). I then decide if I think the Favorite will win by less than that. If so, I picked the underdog there, too. Otherwise I select the favorite. It's really just one extra step.
The idea of this one is that it should be basically a coin flip. If the spread is ideal, then you have an equal chance of getting it right either way. For some of us it is more fun, because without the spread it is hard to guess better than the people that pick the favorites and underdogs. This way you can either be lucky or good and still win.
Note: Technically, there are more things that go into what makes the spread, but you can ignore them. They have to do with what number makes the gambling wagers even out on either side, so in some cases they might not be perfect indicators of a 50-50 chance. An example is if there are lots of Raider fans that are big gamblers living in Vegas compared to Charger fans, the line might be a little biased towards the Raiders. As I said, though, you can usually try to ignore those small biases in making your picks for leagues like this.