Anyone else care to provide some insight? The goal is to build a web based application, sort of like what google calendars is for lack of a better description. (I might need to make a new thread that explicitly states that).
You're asking a question of which there is no right answer.
To write a web based application you will need a server side technology. There are literally hundreds to choose from. Some of the more popular server side technologies include PHP, Ruby (on Rails), Java (JSP/Servlets), and ASP.NET. Others include ColdFusion, Perl, Python, Javascript, Tcl, etc...
Now once you decide on a technology, you will need the appropriate server software installed and configured. PHP is very common and is quite easy to setup. Almost any shared hosting provider will have PHP and isn't a bad place to start learning the ins and outs of web programming.
It's also worth mentioning that there are thousands of frameworks in all those different technologies to help get you going a little quicker.
Finally, once you start getting to the actual UI, you will most likely use a combination of HTML, CSS, and Javascript.
As for Google calendar, its written in Java on the server, and relies heavily on AJAX (XML and Javascript) for some of the cool UI features.
P.S. If you want a cross platform desktop based application (i.e. a downloadable app) - look no further than Java.