Change a web.config programmatically with C# (.NET)

Here it is some code:

var configuration = WebConfigurationManager.OpenWebConfiguration("~");
var section = (ConnectionStringsSection)configuration.GetSection("connectionStrings");
section.ConnectionStrings["MyConnectionString"].ConnectionString = "Data Source=...";
configuration.Save();

See more examples in this article, you may need to take a look to impersonation.