Q:

What is the best Mathematica tutorial for young people?

As Conrad Wolfram said at the TED conference, in the future kids should focus more on new technology. Computers compute better than humans, so we should focus more on thinking and getting the knowledge how to use available software.
I teach programming to my young friend, he is 14. He is very talented, however he still has very much to learn. I wonder how I can teach them to use Mathematica to help with homework and maths materials...
I finished my IT studies. I have only used Mathematica a few times, but I am not an expert.

A:

Mathematica is the best tutorial. It is a discovery tool - just start from something that he knows a bit already and you both take one little step at a time. Just try things.

1st Thing - Try this Link => Hands-on Start to Mathematica
I personally would recommend engaging with him in a project of making an application and submitting it to the Wolfram Demonstrations Project. 

http://demonstrations.wolfram.com/
Check out stuff for kids: Link => Especially this
It could be something simple, but because it is interactive - he may find it fun to play with. I suggest you guys design and make a game. When teens have precise goals it is easier to set them on track especially if it is fun. You can also look through demonstrations and try to figure out how they work. Taking thinks apart - kids like that ;-)

There are many videos here:

http://www.wolfram.com/broadcast/

But, again, Mathematica is the tutorial itself. It has some magic called "free form linguistic input". Basically you type in plane English and it gives you back the code or data. This is very cool for kids and teens. They can see how a concept is getting turned into code. You can find a few examples here:

Link => Virtual talk video
Link => Virtual talk notebook
This maybe a little bit adult level, but you can find some tricks how to teach him.

I generally recommend all talks here - videos & notebooks:

http://www.wolfram.com/events/virtual-conference/2011/presentations/

Mathematica Documentation is full of neat examples.
If he does not have Mathematica he can try using Wolfram|Alpha - it is free:

http://www.wolframalpha.com/
I very much like the idea of teaching programming to children. Below are a standard references for students:
M10: A Student's First Course in Mathematica
Wolfram Education Portal

A:

Affirming Vitaliy's suggestions I'll say something beyond his comprehensive answer and to a certain extent more specific. 
A great mathematician S.Banach used to say (maybe as a joke) that children shouldn't be taught mathematics early because that would be a too sharp tool for them. There is an obvious analogy and this is why children shoudn't be taught Mathematica  too early.  I'm affraid the events such as C.Wolfram's talk at the TED conference make some kind of delusion and I feel similarly when reading (pointed out by J.M.) an interesting discussion Will it rot my students' brains if they use Mathematica? 
Though in general I agree with the statements therein and find Mathematica a great computer system, however one should carefully  consider  WRI employees' arguments concerning  such a delicate issue as teaching.    
To point out helpful resources if one's aim is to be capable doing more than just press the button, it is a good way to read a clear and concise compendium by Richard J. Gaylord:
Mathematica Programming Fundamentals: Lecture Notes
Many programs  at the demonstrations project are certainly useful, however in principle it is much better for  understanding if they come together with Gaylord's excellent 
introduction to Mathematica programming. More throughoutly is just to read the whole book by Paul R. Wellin, Richard J. Gaylord, Samuel N. Kamin (a bit more advanced for the very beginners): 
An Introduction to Programming with Mathematica, Third Edition
If one needs a video tutorial I suggest to start with  something fast and easy, this one by Adam Berry from the Virtual Conference 2011 is good enough :
Introduction to Functional Programming
(note that one has to register to watch it)
I find useful also this video tutorials accompanying  Mathematica Cookbook  by S.Mangano, which presents a wide range of interesting examples of programming from beginners' level to more advanced issues.
At last but not least I suggest that young people have to study also mathematics, since it is (in my opinion) dangerous if one accustoms to use functionality for solving equations without understanding what it really does.

A:

One unconventional but possibly very useful approach it to introduce him to Project Euler.  While many of the newer questions are completely beyond me (mind you that is not saying much), many of the earlier ones are quite approachable.  If your friend has the desire to learn and an interest in puzzles/challenges, this site will grow as he grows.
Most of the problems are best solved by a combination of mathematical logic and programming, and one can see what is possible with computer assistance.
Once a particular problem has been solved you will be able to view other's solutions which opens up whole new lines of thinking and provides exposure to foreign concepts.

The Wolfram Blog and Screencast Gallery are great for showing what Mathematica is capable of, and the Blog provides links to other useful areas.

