Once you rent the movie, you have to move it to your iPhone.
1)Click on your iPhone in the left column in iTunes.
2)Once on the main screen, click the Video tab at the top. In Rented Movies, your movie should be there. In the case of the screen shot, the movie is Blades of Glory.
3)Click move to move the movie to your iPhone. Once you move it, the movie will no longer be in iTunes. You must be connected to the internet to make the move.
David