How do I log into a site with WebClient?

If the problem you are having is you can authenticate but you cant keep the authentication cookie here is a cookie aware version of WebClient.

private class CookieAwareWebClient : WebClient
{
    public CookieAwareWebClient()
        : this(new CookieContainer())
    { }
    public CookieAwareWebClient(CookieContainer c)
    {
        this.CookieContainer = c;
    }
    public CookieContainer CookieContainer { get; set; }

    protected override WebRequest GetWebRequest(Uri address)
    {
        WebRequest request = base.GetWebRequest(address);

        var castRequest = request as HttpWebRequest;
        if (castRequest != null)
        {
            castRequest.CookieContainer = this.CookieContainer;
        }

        return request;
    }
}

EDIT:
The link you gave me uses forms authentication with HTTP POST, I don’t have the time to walk though it but at least it gives you a start with Google.