How to become? Most programming languages suitable for web developement, have mainstream web frameworks. Pick one you like and start learning the programming language simulteniously developing simple web-site. Basic understanding of internet principles is encouraged. Next proceed to data processing (SQL, files) - it will allow you to build simple interactive websites. General understanding of authorization/authentication algorithms would be profitable. Once you will confident with your basic skills or unsatisfied with performance of your site, you could move to more complex topics like caching, optimizations, balance loading etc.
Track your progress by checking the skills below. You will see what other alternatives are open to you and where to read/watch about given skill. Switch to graphical view (roadmap) if you prefer picutures to texts