I would like to find out the roots of Hungarians and Turkish people.
Is there a relationship between those two nations?

Any similarities between the HUngarians and Turks result from the
Turkish Ottoman Empire's occupying Hungary in the 16th century.  The
Hungarians came from the Ural Mountains, whereas the Turks migrated
from Central Asia into Asia Minor (Anatolia), eventually in 1453
conquering Constantinople/Istanbul and then expanding into
southeastern Europe and up to Hungary.
Their languages are entirely different, Hungarian being a Finno-Ugric
language, related to Finnish  - and not much else -, whereas Turkish
is an altaic language, still closely related to that of the Turkmen in
Turkmenistan and Usbekistan.
But the Hungarians are a little pleased that only in Turkish they are
referred to by their own name for themselves: Magyar.
Websites on Hungarian/Turkish people/language will add a lot more.

Two articles referring to the possible linguistic relation between
Uralic and Altaic languages:

http://www.infoplease.com/ce6/society/A0850158.html

http://en.wikipedia.org/wiki/Ural-Altaic_languages

Hey, fp-ga, that's good, thanks.  Didn't know that (obviously).

If you want an even more bizarre link look at the lingustic
similarities between Turkish, Finnish and Basque- there is a real
brain twister

both of the nations used to live in the mid asia before they
immigrated to europe. the turks who came to anatolia through iran and
arabia became muslims nad the hungaerians who went through the
cafcasus(or however its spelled) became christians. both nations have
similar roots.

Thank you for all the comments and the web links those are useful.