The best way to think about switches is to think of a light switch. Unless you have one of those fancy dimming lights, there are only two options; It's either on or off. It can't be anything else. Game switches are the same way, but instead of turning on a light, it makes stuff happen. What kind of stuff? Well, let's have an example, shall we?
Say we want to have a quest. Some town person wants you to go kill a monster or something. First off, we'd need the townsperson to say something different after you accept the quest. You wouldn't want him to keep asking you to do the same quest over and over again, unless he was written to be incredibly amnesiac, but for the sake of this tutorial, he isn't.
In this specific case, a self switch would be the best thing to use. A self switch is like a normal switch, only it affects the event it's applied to and nothing else. A normal switch can affect all events, which would be a bit overkill since we're only dealing with one guy. So after the quest dialogue, you'd use the Control Self-Switch Event Command and turn Self-Switch A ON.
Next, you'd make another event page, but this time check the box in the upper left that says Self Switch ____ is on. It should be set to A automatically. This is where you would write the dialogue he would say after you've already accepted the quest.
What about after you defeat the monster for him? This time you'd use a regular switch. Remember how I said Self-switches only work on the event they're on? In order for the monster's death to affect the townsperson, you need to pick a switch using the Control Switch Event Command. When you click the single dialogue box (as only a single switch is needed. I've personally never used batch. I'm sure it has its uses though.) a numbered list appears. You can name your switches in the box at the bottom. It isn't required, but it helps alleviate confusion later. After you choose a switch, set it to ON.
You'll then need another event page for the townsperson. This time, instead of checking the self-switch box, you'd check one of the normal switches at the top. On this page, you would put the dialogue for completing the quest, as well as any rewards to give to the player. After that, you'll probably want to make another self-switch so he doesn't keep giving you the items. This time, set self-switch B to on, make another event page, and check the self-switch box, making sure B is selected this time.
PICTURES TO BE ADDED LATER
Hopefully you got the gist of it. Switches are one of the fundamental aspects of rpg maker, and you can do a lot more than just a simple quest with them. There are some things that you can't do, though, which brings us to.....