Creating a site like StackOverflow is, while hardly brain science or rocket surgery, not something I would recommend for a complete beginner unless you have a lot of time to spend on the project as you will need to learn the relevant server-side skills (i.e. some programming language for the logic layer and database for storage if you are not familiar with DBs elsewhere), client side coding (javascript and DOM), the masses of security issues that you will need to be aware of, and (if you want your site to hit the big time) scalability issues.
If you want to do this as a learning exercise more than anything else then it is probably a good choice of project, but if you are looking to get a decent quality site up and running in good time you would be far better off searching for an existing solution that comes close to what you want - there are no doubt many F/OSS projects out there that at least come close.
As for further advice on how to make the first steps, you would need to let us know where you are starting from. What previous programmnig/design experience do you have? In what languages and environments? Much database knowledge/experience? With multi-user systems? Do you have any OS/environment preferences? ...?