How to open a web page from my application?

For desktop versions of .NET:

System.Diagnostics.Process.Start("http://www.webpage.com");

For .NET Core, the default for ProcessStartInfo.UseShellExecute has changed from true to false, and so you have to explicitly set it to true for this to work:

System.Diagnostics.Process.Start(new ProcessStartInfo
    {
        FileName = "http://www.webpage.com",
        UseShellExecute = true
    });

To further complicate matters, this property cannot be set to true for UWP apps (so none of these solutions are usable for UWP).

Accepted answer no longer works on .NET Core 3. To make it work, use the following method:

var psi = new ProcessStartInfo
{
    FileName = url,
    UseShellExecute = true
};
Process.Start (psi);