C#

byte[] buffer = new byte[1024];
int read = 0;
inputStream.Position = 0;
while((read = inputStream.Read(buffer, 0, buffer.Length)) != 0) {
    outputStream.Write(buffer, 0, read);
}
outputStream.Flush();

public void DownloadFile(System.Uri url, string filePath, long sz)
{
    Stream r = null;
    Stream output = GetFileStream(filePath);

    // 1. create a web request
    System.Net.WebRequest request = System.Net.WebRequest.Create(url);
    System.Net.HttpWebRequest hrequest = (System.Net.HttpWebRequest)request;

    //This is the key right here
    //This reads the file that already exists
    //and gets the length of the file
    //and resumes from where it left off
    hrequest.AddRange(Convert.ToInt32(w.Length));

    hrequest.UserAgent = "Mozilla/4.0 (compatiable; MSIE 7.0; Windows NT 6.0)";

    System.Net.WebResponse response = null;
    try
    {
        using (response = request.GetResponse())
        {
            using (r = response.GetResponseStream())
            {
                using (output)
                {
                    WriteToFile(r, output, sz, w.Length);
                }
            }
        }
    }
    catch (Exception ex)
    {
        // on error, delete the partially downloaded file
        File.Delete(filePath);
        throw new Exception("Could not save " + url, ex);
    }
    finally
    {

    }
}


private Stream GetFileStream(string filePath)
{
    string fileDirectory = filePath.Substring(0, filePath.LastIndexOf(@"\"));
    if (!Directory.Exists(fileDirectory))
        Directory.CreateDirectory(fileDirectory);

    if (File.Exists(filePath))
        return File.Open(filePath, FileMode.Append);
    else
        return File.Create(filePath);
}


private void WriteToFile(Stream response, Stream output, long sz, long initSize)
{
    DateTime startTime = DateTime.Now;

    if (sz == 0)
        return;

    byte[] buffer = new byte[1024 * 64];
    long read = 0;
    long totalRead = initSize;

    while ((read = response.Read(buffer, 0, buffer.Length)) > 0)
    {
        output.Write(buffer, 0, Convert.ToInt32(read));
    }

    w.Flush();
}