Simple means of making a function non-blocking / async in C#?

SmtpClient has SendMailAsyncso using it instead of Send will unblock the UI thread while sending but you can still handle any exception that may occur:

private async void button_Click(object sender, EventArgs e)
{
   await SendEmailAsync(address, subject, body)
}

public async Task SendEmailAsync(string toAddress, string subject, string body, string code = null) 
{
    try 
    {
        var fromAddressObj = new MailAddress("[email protected]", "Name");
        var toAddressObj = new MailAddress(toAddress, toAddress);
        const string fromPassword = "Password";

        var smtp = new SmtpClient {
            Host = "smtp.office365.com",
            Port = 587,
            EnableSsl = true,
            DeliveryMethod = SmtpDeliveryMethod.Network,
            UseDefaultCredentials = false,
            Credentials = new NetworkCredential(fromAddressObj.Address, fromPassword)
        };
        using (var message = new MailMessage(fromAddressObj, toAddressObj)
        {
            Subject = subject,
            IsBodyHtml = true
        }) 
        {
            message.Body = body;
            await smtp.SendMailAsync(message);
        }
    }
    catch (Exception e) 
    {
        Elmah.ErrorSignal.FromCurrentContext().Raise(e);
    }
}

If the synchronous part of the async method (the part before the await) still manages to block the UI thread you can offload it to a ThreadPool thread:

private async void button_Click(object sender, EventArgs e)
{
   await Task.Run(() => SendEmailAsync(address, subject, body))
}

Notes:

• Don't fire up a Task without awaiting it unless you're in a situation where you can't use await (a UI event handler is not one of those cases)
• async void is only appropriate for UI event handlers. Don't use it anywhere else.