Using System.Net.Webclient, you can easily download the file on the Web url, make sure that the file path is relative to the web url e.g. If the example.jpg is hosted in the root of www.example.com then use like,
WebClient wc = new WebClient();
wc.DownloadFile("http://www.example.com/example.jpg", @"C:\example.jpg");
You need to pass the local physical path to avoid open/save file dialog.
Find more info
here