Yum has a feature called 'groupinstall' that will help you here. What you can do is perform the minimal install, and then after booting to the console perform the actions described on this page:
http://docs.fedoraproject.org/en-US/Fedora/15/html/Installation_Guide/sn-switching-to-gui-login.html
The short story is that you'll be installing the "X Window System" and "GNOME Desktop Environment" groups of packages via yum groupinstall.
The instructions on that page also walk you through changing the "default run level" from 3 to 5, this will make your system boot in to a graphical system rather than to the console. However, I noticed a small problem with those instructions. They walk you through the process of editing the text file by using vi, however they don't specify that you need to hit Esc to switch from insert mode to command mode. You can follow the instructions on that page, but be sure to hit the Esc key before doing what is described in step 6.