Full stack web developers are hot shit, and will continue to be hot shit for as long as companies act like simple minded cheapskates. Also known as forever. To be hired to do the work of three or four people, for 1/2 the salary that it would cost to employ those specialist people (or easily 50% premium over market), learn this stuff:
HTML/CSS
We want you to understand the box model, understand the css attributes, what the base stylesheets are used by browsers, how they're defined in a page. You'l lneed to learn about CSS management engines that compile up css files to send to the browser from normalized data.
Here's a place with much info:
http://learn.shayhowe.com/advanced-html-css/ Design and CSS are well addressed here:
http://www.csszengarden.com/ Javascript
Learn its basic syntax. Learn about about how its inheritance model works. Figure out what .prototype is vs. what an object is, how things layer. What is a context? Why is it important? How does it affect memory usage? How about timeouts and intervals? Learn how you can modify and extend html objects with javascript to add and change behavior. Learn about making XHTTPRequests (ajax). Learn how to modify the page that you're on. Look up templating systems that work in javascript (like mustache)
Tons of resources, simulators, answers to questions...
http://www.w3schools.com/js/ Programming language:
I like perl, but it doesn't matter unless you want to ask me questions about the library support and details. Ruby, python, php, perl, its not particularly important. This will be the back end language that will provide the server side logic that backs the dynamic features of the site. You'll probably be using a fastcgi interface of some sort.
Learn about some kind of web structure framework that works in the language you've chosen to specialize in for the moment. this is probably model view controller type stuff. View (templating) is particularly important to learn about interacting with on the design and page management level.
Learn about interfacing with at least one relational database (mysql, postgres) and one document database (mongo, couchdb...) and how to interact your program with the data stored in that database.
Web server
Learn to install and configure nginx. Get it to run your server side programs. Get it to deliver static content. Configure a reverse proxy to serve your static content and proxy to a different web server instance to deliver dynamic processing.
Operating Systems
You'll want to be deploying on something like Ubuntu. Spin yourself up a VM (virtualbox is good and free) and become familiar with operations like updating the system software, finding things on the system, installing and configuring software like nginx and the server side program and its support libraries.
Version control
Learn git. Learn how to branch. Use them. Learn how to merge branches. Learn how to use git-bisect to find revisions where changes occured semi-automatically. Be able to explain how git layers, moves changes around. Learn how to make git compress and optomise. Explain the risks in doing odd bits. Read and internalize this book.
https://git-scm.com/book/en/v2 Performance/scaling
Caching. Redis, memcached, what do they do, how do you use them, why do you use them?
Cloud systems. Get yourself an amazon AWS account (they're cheap if not free) and learn how to use their systems to make all the stuff above that you learned to do on your VM work on THEIR systems. Learn how to make that deploy smoothly with minimal effort.
Project management
I bet you thought that was something people dedicated to project and/or management did. Nope. A good part of the success of any developer - particularly one that is interfacing with many different things and trying to balance them - is project management. Study the principles. Learn how to stay organized. Learn how to mindmap. Mindmap. You need to learn how to use mindmaps. Did I mention mind mapping? Its important.
FINALLY
MAKE SOMETHING. You have not successfully learned this shit until you make something. it should use all of the things that you learn in this list. And you should be able to in only a few steps, take what you have written and an instance up and running on a fresh cloud server that has never seen your code before.