Instead of being bound to specific programming languages and the look and feel of a particular operating system, you can put your killer application in the browser and run it in the cloud, as a webapp. Welcome to the wonderful world of web development.
HTML and CSS: The first thing you need to know to build any web site is HTML (the page markup that makes up web pages) and CSS (the style information that makes that markup look pretty). HTML and CSS are not true programming languages—they're just page structure and style information. However, you should be able to author simple HTML and CSS by hand before you begin building web applications, because a web page is the frontend to every webapp. This HTML tutorial is a good place to start.
JavaScript: Now that you can lay out a static web page with HTML and CSS, things get fun—because it's time to learn JavaScript. JavaScript is the programming language of the web browser, the magic that makes dynamic in-page effects go. JavaScript is also the stuff of bookmarklets,Greasemonkey user scripts, and Ajax, so it's the key to making all sorts of web goodies. Start learning JavaScript here.
Server-side scripting: Once you're good at making things happen inside a web page, you're going to need to put some dynamic server action behind it—and for that, you'll need to move into a server-side scripting language, like PHP, Python, Perl, or Ruby. For example, to make a web-based contact form that sends an email somewhere based on what a user entered, a server-side script is required. Scripting languages like PHP can talk to a database on your web server as well, so if you want to make a site where users can log in and store information, that's the way to go. Excellent web development site Webmonkey is full of tutorials for various web programming languages. See their PHP Tutorial for Beginners. When you're ready, check out how to use PHP to talk to a database in WebMonkey's PHP and MySQL tutorial. PHP's online documentation and function reference is the best on the web. Each entry (like this one on the strlen function) includes user comments at the bottom which are often as helpful as the documentation itself. (I happen to be partial to PHP, but there are plenty of other server-side scripting languages you might decide to go with instead.)
Web frameworks: Over the years, web developers have had to solve and resolve the same problems and rewrite similar code to build dynamic web sites. To avoid making everyone reinvent the wheel for every new web development project, some programmers have come up with development frameworks that do some repetitive work for you. The popular Ruby on Railsframework, for example, takes the Ruby programming language and offers a web-specific structure for getting common web application tasks done. In fact, Adam used Rails to build his first serious (and impressive!) web application, MixTape.me. Here's his take on how to build a web site from scratch with no experience. Other popular web development frameworks include CakePHP (for PHP programmers), Django (for Python programmers), and jQuery (for JavaScript).