using Vonage;
using Vonage.Request;

var credentials = Credentials.FromApiKeyAndSecret(
txtAPIKey.Text,
txtAPISec.Text
);

var VonageClient = new VonageClient(credentials);
var response = VonageClient.SmsClient.SendAnSms(new Vonage.Messaging.SendSmsRequest()
{
To = txtTO.Text,
From = txtFrom.Text,
Text = txtText.Text
});
MessageBox.Show("sms send successfully");

Full Tutorial: