I am not a big organization or something, but I just want to build a site which will behave like stack overflow. I like the way this site is.
Thanks for your help
It's totally ok to use SE platform as a regular user but not the API.
See other questions about SE sites in languages other than English:
The Stack Exchange API can't be used in this manner, and there are currently no options for you to run an SE site on your own hardware.
You could try an open source alternative (although I don't know how good it is): OSQA.