The missing ingredient

It didn't work!

Followed that tutorial right from the first line to the last one. Did everything it said, but still didn't get what you were looking for? Believe me, it was supposed to be that way. Step by step code execution on the cli is not what it takes to be a hacker. Every wireless adapter, computer system, operating system, and wireless network is different. There is no fixed set of code which is bound to work with all wifi's on all machines. Hacking is like mathematics. Knowing the formula doesn't mean you can solve all the problems, and seeing the solution of one problem will definitely not help you with another one. So, when you are hacking a WEP wifi network, what are you actually doing?

What were you doing?

Firstly, you are capturing the packets that the wifi network is... like throwing away in the air. The sole purpose of those packets is to indicate its presence. Airodump just takes all the packets that come its way and collects them. These packets usually contain some useful information.Secondly, you are using a program to extract the password from the captured data packets.

How were you doing it?

Now, firstly, we do something not completely required. We turn on monitor mode. Its just like creating a virtual interface which you'll use solely for monitoring purpose. Now this task is achieved my using airmon-ng and the new interface is called mon0.
Secondly, we use airodump-ng to capture packets from mon0 and store them in a file. Finally, we use aircrack-ng to use the data in the dump file to extract the password.

What problems are you going to face?

Most of the time, I have seen beginners are unable to configure their machines properly to a state where they can execute the commands. For this, look at the other tutorials.I am assuming you have Kali completely setup and running fine and accepting your wireless cards. So the problems-

Not enough data packets.
Not WEP encrypted. (i.e. WPA or WPA-2)
Hidden

Now the last two problems will be dealt with in the tutorials to come. The first problem is very common and there is no straightforward way to deal with it. You can only try to speed up the data capture rate. There are a lot of ways to do that. A lot depends on how far you are from the network. I am writing a complete tutorial for this. But remember, hacking requires patience. You're gonna need it when you get to higher levels where you will bruteforce networks for the passwords.
For now, here is a great tutorial on getting data packets fast.