Assuming the files you want to update are located in the application's bin directory, you can just copy the new files into the directory.
ASP.NET makes a "shadow copy" of the files, and loads them from the copy. When you update the files, it creates a new AppDomain to service any new requests, and signals the previous AppDomain to shut down as soon as it has finished servicing any current requests.
Components of your application can be updated while the server is online and clients are connected. The framework will use the new files as soon as they are copied to the application. Removed or old files that are still in use are kept in memory until the clients have finished.