How can I build a social network and make sure that I'm not infringing on any copyrights (ex. Facebook)?

You will want to retain a patent attorney to conduct a patent search for you. Specifically, you will want to conduct a patent infringement search, also known as a freedom-to-operate search or a right-to-manufacture search.

Copyright only protects a specific expression of an idea so you can create a social network as long as it doesn't copy the look and function of any other platform. You will also be subject to the issues that many of these companies are facing right now, such as whether or not to allow government access to information your users post on your site and to what extent you are liable if someone posts something illegal on it.

You should work closely with an attorney. That is not a question with a simple answer. There are many ways you could get into trouble.

Although copyright can be a potential issue, you may want to give more attention to whether you might be infringing on patents held by social networks. This will require you to search for patents held by the social networks and then compare their patent claims against your proposed network.