Get a small computer -- a Raspberry Pi, or a Zotac AD-11, for example.
Then hook the robot arm and camera up to that computer.
Then write some server software on that computer to serve web pages to the Internet, and talk to the arm/camera on the other side.
You'll probably want to use an existing web server framework -- ASP.NET on Windows, Apache on Linux with PHP, WSGI on Linux with Python, Tomcat on either with Java, or whatever your preferred language/framework is.