To create a Silverlight application in Visual Studio, all we have to do is to go to File->New Project and select "Silverlight application".
All the details including the name of the project, it's location in the filesystem, etc can be configured by changing values at the bottom of the window.
When we create an application, the wizard will prompt us to find out if we want to create just a Silverlight application (I am presuming for the desktop), or we want to create an ASP.NET application which is a web application bundled with the Silverlight app. If we choose the latter, we will have two applications. One the Silverlight app, and the web app. The web app will run on the browser, and will pull the Silverlight app for running in the Silverlight plugin in the browser.
Since Silverlight has a plugin, it seems very similar to a Java Applet, but I am sure they have taken more care to allow it to interact with Javascript, etc on the webpage.