This action is going to send a mail so we need to add a reference to

System.Web

Then add the following implementation:

using System;
using System.Web.Mail;
using Ant.ContentEntry;
using Ant.ContentEntry.ClassInformation;
using Ant.ContentEntry.FieldDisplayers;
using Ant.ContentEntry.Converters;
using Ant.Database;
using Ant.Security;
using Ant.Workflow;

namespace HowTos
{
    /// <summary>
    /// This is an example action
    /// </summary>
    [ClassOverview]
    public class HowToAction : Action
    {
        private string message;
        AuthenticatedUser user;
        /// <summary>
        /// Constructor, taking a user which is supplied whenever 
        ///        this action is constructed by the workflow engine
        /// </summary>
        /// Logged on user
        public HowToAction(AuthenticatedUser user)
        {
            this.user = user;
        }
        /// <summary>
        /// Message of the email
        /// </summary>
        [PropertyInformation(typeof(StringConverter), typeof(InputEntry), true, 0)]
        [PropertyLanguage(PropertyLanguage.English, "Message", 
            "This is the message of the email", "You must enter a message")]
        public string Message
        {
            get {return message;}
            set {message = value;}
        }
        #region Action Members
        /// <summary>
        /// Terminates the action, in this case takes no action
        /// </summary>
        public void Terminate(ActivityInstance instance, Ant.Database.AntConnection connection, 
            Ant.Database.AntTransaction transaction, ref string state)
        {
        }
        /// <summary>
        /// Starts the action, returns true to say that a response is to be waited for
        /// </summary>
        public bool StartAction(ActivityInstance instance, Ant.Database.AntConnection connection, 
            Ant.Database.AntTransaction transaction, User performer, ref string state)
        {
            // Sends the mail
            SmtpMail.SmtpServer = "****";
            
            MailMessage mail = new MailMessage();
            mail.To = "***";
            mail.From = "****";
            mail.Subject = "Test";
            mail.Body = message;
            
            SmtpMail.Send(mail);
            
            // add a response which is picked up in ProcessActionResults, 
            // this is how a synchronous action is implemented
            instance.AddResponse(this.user, performer, "Response received in ProcessActionResults", 
                "", connection, transaction);
            return true;
        }
        /// <summary>
        /// Gets the URL for context sensitive help, returns null as there is no help for this action
        /// </summary>
        /// 
        public string GetHelpUrl()
        {
            return null;
        }
        /// <summary>
        /// Gets the name of the action
        /// </summary>
        public string GetActionName()
        {
            return "How to action";
        }
        /// <summary>
        /// Gets the short description of the action
        /// </summary>
        public string ShortDescription
        {
            get
            {
                return "Sends a message";
            }
        }
        /// <summary>
        /// Gets the long description of the action
        /// </summary>
        public string LongDescription
        {
            get
            {
                return message;
            }
        }
        /// <summary>
        /// Process the results of the action
        /// </summary>
        public string ProcessActionResults(ActivityInstance instance, Ant.Database.AntConnection connection, 
            Ant.Database.AntTransaction transaction, User performedBy, string results, ref string state)
        {
            // nothing to do here, just return the name of the transition to fire
            return "Next";
        }
        /// <summary>
        /// Gets the names of transitions that this action supports
        /// </summary>
        public System.Collections.ICollection GetRequiredTransitionNames()
        {
            return new string[] {"Next"};        
                // only one transition, matches string that is returned from ProcessActionResults
        }

        #endregion
    }
}
        

The key points of the implementation have been picked out in comments. As this is a synchronous action, ProcessActionResult has nothing to do and StartAction posts a response for the workflow engine to pick up on.