How to detect are the applications trying connnect to some websites?

Task Managers and process list

Hello all, I am developing a small module of anti-malware project. I have to develop a module which scan through all the Process in Task Managers, for identify are them connect to some websites? And what website are them connecting?

Does any body know the walk a rounds? Or I hope some you guys can point me some reference to do research.

Appreciate and have a nice day~