You place the game inside the sleeve with the barcode on it, then put the sleeve in the cardboard piece, then put that in the envelope they sent the original game in, seal it and put it in your mail box, etc. to mail it out.
This is from the FAQ section, its best to check for stuff there before asking a question here.
"If you've lost the sleeve to a game, to ensure we can return the game against your account once it is received in our shipping center, please do the following:
Write your first name, last name, and e-mail login on a sheet of paper, along with the title of the game you're returning.
Place the sheet of paper into the mailing envelope with the game.
Mail the game back to GameFly as usual. Once we receive the game, we will create a new sleeve and then return the game. It will take more time to process your return.
In the future, please be sure to hang onto the game sleeve so there is no delay in your return processing.
If you've lost the pre-paid mailing envelope, please request one by going to Report A Shipping Problem. Once there, select the specific game you need a return envelope for and then select I lost the game's shipping envelope. We will be more than happy to send you another one."