Here is a rough outline of my thoughts on what do and how to do it to really build your web developer skillset.
For the front end, there are really three main components:
- HTML (make sure you learn about DOCTypes and how to make valid websites)
- CSS - How to style pages, this is really a core skill these days. Table layouts are not 'wrong' anymore as most browsers now agree on how to build them, but as you do work if you client is savvy they will be very unimpressed with them and you'd do well to know how to do a layout using just CSS.
- Javascript - As sites become even more interactive JS is a core tool that you'll call upon for almost every project.
- Javascript libraries - These are things like jQuery, Prototype, moo, YUI, things which extend JS and simplify your work in implementing different things.
For the backend, you'll be best served by picking a language and focusing on it: PHP is probably the easiest in terms of entry costs. ASP.net requires a bit more setup for learning to work with it. Ruby on Rails is up and coming as a backend coding language, quite hot among web 2.0 companies but it isn't near as popular as PHP and ASP.net.
In these languages you'll find frameworks which provide a good basis for web applications. CodeIgniter, CakePHP and a whole host of others currently exist. Again you're just going to have to begin playing around and dive into them.
At a lower level, when writing the sites, you need to understand Object Oriented programming as well as other core Computer Science elements.
For websites, content management systems are a main component in projects these days. Wordpress, Drupal, ExpressionEngine are just a few. You'll do well to research these and begin working with them. Some are rather intimidating and frustrating to work with.
The next step is to begin learning to use other sites and their APIs. Like writing a Facebook application, or a Twitter application. To learn these, a good plan is to reinvent the wheel. Want to learn the Twitter API? Build a web twitter client. What to learn Facebook? Make a simple game.
Etc.