Unfortunately the free trial starts as soon as you sigh up. Your games will probably ship out between today (Monday) and Wednesday. It will then take 2-4 days for shipping. I think best scenario would be that you'll have 4 maybe 5 days to play the games. There are times when GameFly is really slow and takes the better part of a week to send the games.
In my opinion the free trial does a total disservice to the trial user, existing members and GameFly itself.
Anyone who hasn't signed up yet would be much better off using the URL below to get a buy one month, get one month free special.
Good luck and good gaming.