Как сделать HTTP POST веб-запрос

Простой запрос GET

using System.Net;

...

using (var wb = new WebClient())
{
    var response = wb.DownloadString(url);
}

Простой запрос POST

using System.Net;
using System.Collections.Specialized;

...

using (var wb = new WebClient())
{
    var data = new NameValueCollection();
    data["username"] = "myUser";
    data["password"] = "myPassword";

    var response = wb.UploadValues(url, "POST", data);
}

MSDN имеет образец.

using System;
using System.IO;
using System.Net;
using System.Text;

namespace Examples.System.Net
{
    public class WebRequestPostExample
    {
        public static void Main()
        {
            // Create a request using a URL that can receive a post. 
            WebRequest request = WebRequest.Create("http://www.contoso.com/PostAccepter.aspx");
            // Set the Method property of the request to POST.
            request.Method = "POST";
            // Create POST data and convert it to a byte array.
            string postData = "This is a test that posts this string to a Web server.";
            byte[] byteArray = Encoding.UTF8.GetBytes(postData);
            // Set the ContentType property of the WebRequest.
            request.ContentType = "application/x-www-form-urlencoded";
            // Set the ContentLength property of the WebRequest.
            request.ContentLength = byteArray.Length;
            // Get the request stream.
            Stream dataStream = request.GetRequestStream();
            // Write the data to the request stream.
            dataStream.Write(byteArray, 0, byteArray.Length);
            // Close the Stream object.
            dataStream.Close();
            // Get the response.
            WebResponse response = request.GetResponse();
            // Display the status.
            Console.WriteLine(((HttpWebResponse)response).StatusDescription);
            // Get the stream containing content returned by the server.
            dataStream = response.GetResponseStream();
            // Open the stream using a StreamReader for easy access.
            StreamReader reader = new StreamReader(dataStream);
            // Read the content.
            string responseFromServer = reader.ReadToEnd();
            // Display the content.
            Console.WriteLine(responseFromServer);
            // Clean up the streams.
            reader.Close();
            dataStream.Close();
            response.Close();
        }
    }
}

Вам нужно использовать класс WebRequest и GetRequestStream.

Здесь приведен пример.

Это полный рабочий пример отправки/приема данных в формате JSON, я использовал VS2013 Express Edition

using System;
using System.Collections.Generic;
using System.Data;
using System.Data.OleDb;
using System.IO;
using System.Linq;
using System.Net.Http;
using System.Text;
using System.Threading.Tasks;
using System.Web.Script.Serialization;

namespace ConsoleApplication1
{
    class Customer
    {
        public string Name { get; set; }
        public string Address { get; set; }
        public string Phone { get; set; }
    }

    public class Program
    {
        private static readonly HttpClient _Client = new HttpClient();
        private static JavaScriptSerializer _Serializer = new JavaScriptSerializer();

        static void Main(string[] args)
        {
            Run().Wait();
        }

        static async Task Run()
        {
            string url = "http://www.example.com/api/Customer";
            Customer cust = new Customer() { Name = "Example Customer", Address = "Some example address", Phone = "Some phone number" };
            var json = _Serializer.Serialize(cust);
            var response = await Request(HttpMethod.Post, url, json, new Dictionary<string, string>());
            string responseText = await response.Content.ReadAsStringAsync();

            List<YourCustomClassModel> serializedResult = _Serializer.Deserialize<List<YourCustomClassModel>>(responseText);

            Console.WriteLine(responseText);
            Console.ReadLine();
        }

        /// <summary>
        /// Makes an async HTTP Request
        /// </summary>
        /// <param name="pMethod">Those methods you know: GET, POST, HEAD, etc...</param>
        /// <param name="pUrl">Very predictable...</param>
        /// <param name="pJsonContent">String data to POST on the server</param>
        /// <param name="pHeaders">If you use some kind of Authorization you should use this</param>
        /// <returns></returns>
        static async Task<HttpResponseMessage> Request(HttpMethod pMethod, string pUrl, string pJsonContent, Dictionary<string, string> pHeaders)
        {
            var httpRequestMessage = new HttpRequestMessage();
            httpRequestMessage.Method = pMethod;
            httpRequestMessage.RequestUri = new Uri(pUrl);
            foreach (var head in pHeaders)
            {
                httpRequestMessage.Headers.Add(head.Key, head.Value);
            }
            switch (pMethod.Method)
            {
                case "POST":
                    HttpContent httpContent = new StringContent(pJsonContent, Encoding.UTF8, "application/json");
                    httpRequestMessage.Content = httpContent;
                    break;

            }

            return await _Client.SendAsync(httpRequestMessage);
        }
    }
}

Простой (однострочный, без проверки ошибок, без ожидания ответа) решение, которое я нашел до сих пор

(new WebClient()).UploadStringAsync(new Uri(Address), dataString);‏

используйте с осторожностью!