Sounds like the best solution is to have an entry page that has 2 little flags on it - one Greek, and one English. Caption under each flag should say something like "View this site in xxxx".
If they click on the Greek flag, set a language cookie and then redirect them them to the Greek transaltion. Do the same thing for the English.
You'll want the fist thing on the entry page to be a check for the cookie and route them accordingly. so the next time they come there, they go directly to the right translation.
On the home page for each translation, you should also have the flag that allows them to go to the other translation,