You need to look into the concept called "URL Re-writing".
Because of the way that IIS behaves you typically handle this with some configuration settings in the web.config and create "virtual" URLs that your application handles. Typically, you create a page name that specifies the functionality you want and you parse the URL to get the data that would normally be in querystring parameters. So you could have a URL like this:
mywebsite.com/12/DoSomething.aspx
You translate this into a real URL to some page with 12 as the querystring parameter. I haven't do this kind of stuff myself so my suggestions might not be entirely correct, but that's the general idea. I've seen several tutorials and articles about this online so you shouldn't have much problem finding a detailed explanation.
A general search will likely bring back lots of results that apply to other web servers so try a
search on searchdotnet.com for .NET specific results.
-Peter