There are no formal educational or licensure requirements to become a web developer. However, many colleges and trade schools offer coursework in web development. There are also many tutorials and articles, which teach web development, freely available on the web - for example: Basic JavaScript
Even though there are no formal educational requirements, dealing with web developing projects requires those who wish to be referred to as web developers to have advanced knowledge/skills in:
HTML/XHTML, CSS, JavaScript and jQuery.
Server/client side architecture like all or some of the above mentioned.
Programming/Coding/Scripting in one of the many server-side languages or frameworks (e.g., Perl, Python, Ruby, PHP, Go, CFML - ColdFusion, Java, ASP, ASP.NET, Node.js)
Ability to utilize a database
Creating single-page application with use of front-end tools such as EmberJS, ReactJS or AngularJS