turn based using email is the simplest method.
Just save out all game data to a .txt file.
then Have the user simply send an email with the .txt file as an attachment. Sure, you could get fancy and use a third-party tool to automatically send the email, but some users might not like having a program automatically sending/reading emails.
Another option would be to use FTP. But there are issues there too. Some sites have user limits. One way around it would be for each user to have there own site for writing files to, but make those files read only to other users. But you could still run into bandwidth issues and timing.... can't play real time at all. Maybe one turn every 5 minutes or so.
internet gaming group