Let's face it - the web is a less fun place without Flash. There are plenty of sites that make use of it, and while we have projects to build a free implementation, it's not quite there yet.
So here, I'm going to try and show you how install Flash Player on Fedora 7 as quickly as possible. The process should be pretty simple, but does require use of the terminal. You might want to get one open right now.
$ su -
[[Enter your root password when prompted]]
# rpm -Uvh http://fpdownload.macromedia.com/get/flashplayer/current/flash-plugin-18.104.22.168-release.i386.rpm
That one hit command should download and install the RPM version of the current Flash Player at the time of writing. A quick restart of your browsers should complete the installation, and Flash should work.
You may want to browse about:plugins in Firefox (and similar browsers), to check it is installed. You should see something like this:
If you get that, all is well and Flash is installed. Have fun!