Asp.net or Java ?

My company is considering whether to go the Asp.net or Java route for web based database applications. I would like to get a further a better understanding of Java. With ASP.net you have to set up a server with the dotnet framework and configure IIS. My understanding is that with Java database applications you create an applet and embed it in a HTML page and give you users a shortcut to the HTML page. IE has Java embedded in it so no setup is required on the server. Is this correct?

No.

ASP.NET is a language developed entirely for server applications. It only runs on MSs IIS. (I think there are extensions to Apache so ASP can run, but not yet extensions for ASP.NET). It is executed on the server and outputs HTML code which is sent to the client.

Java is a multi-function language. You can develop real applications that are cross-platform compatible without recompiling. You can develop applets, which are apps embedded in a HTML page. They are executed on the clients machine by a virtual machine that is integrated in the browser. IE comes with a VM. You can download Sun's VM for IE and Mozilla and I think Opera too. All browsers should do that automatically.
But the equivalent of ASP.NET in the Java world is the servlet. This is an app that runs on the server and is invoked by the server application which can be IIS, Apache or any other server application, nearly all can invoke servlets. Servlets generate HTML output which is sent to the client.
You need a VM on the server to run servlets, but it is easily obtainable from Sun.

Examples of pages that use ASP.NET:
microsoft.com

Examples of pages that use servlets (jsp=Java Server Page):
sun.com, starwars.com, the w3 CSS validator

Advantages of ASP.NET:
Can contain pure HTML which is sent unprocessed. Servlets must ouput everything via some print statements.
Needs not be recompiled when the code changes. (not sure)

Advantages of servlets:
The bytecode runs faster than the completly interpreted ASP.NET languages. (not sure)
Not limited to MS servers.

Other alternatives:
CGI-scripts, esp. in PERL.
PHP

One thing CornedBee forgot to mention was the use of JSP pages. This are java's version of asp pages. They can be used in conjunction with servlets and contain both html and java code, and again are translated by the server so no plugin for the user is needed.

Ah, I thought JSP and servlets were the same.

java for sure, use JSP and Servlets and you have all powerfull of java in and out the internet!