Keep the website running while you make changes. 
Make sure your module does not have a cachetime set. 
Login as host to avoid caching.
Use CTRL+F5 in the browser to make sure you clear the broswer cache on refreshes.

hdany wrote Thanks for your answer , but I haven't found the tutorial you were talking about. I did come across on some tutorials posted by Michael Washington , but they are about creating modules and using Linq. This does not help me. I didn't  understand how to use Web Application Project since it is already integrated in VS 2005 SP 1 and it is a standard feature in Visual Studio 2008 which I am using. Can you please be more specific ? or post a link to the tutorial you are talking about ? I would have expected something like a setting in web.config or caching , somehow , in order to only compile the codebehind file I modified instead of the whole project all over again.

If you are using WAP, then John's suggestion works. Otherwise browse Michael's tutorials. He has written tutorials for both WSP and WAP approaches.

Someone sounds a little frustrated ;)  Startup of DNN is always relatively slow, but the suggestions I gave do help.

In VS 2008 you can create WAP or WSP projects.  The DotNetNuke website solution is a WSP, as are most of the core modules.

Another thing you may want to try is clearing your VSWebCache.
You can also use FileMon to try and get an idea of what is happening at startup.

Also try running the website normally, then open the code-behind file with notepad, make your change and refresh. 
If that works then you will know it is something in the VS environment.
I often use Ultra-Edit (a text editor) when developing to make quick changes.

Getting a brand new computer will probably work too.  I should have thought of that. :0