ok fellow new-linux user...I just got through with this battle...
Here's the steps.
Go to http://www.winehq.com
and look in the top right corner. There's a link under "latest release" (currently 20030709). Click on it and on the page it takes you to, use the first link to download a tar.gz file.
You should be able to open the tar file and find an "extract all" button. It will ask you where to extract it to...select a place. It will then make a directory there called wine[version] (ie wine-20030709). Open up a terminal window by right-clicking your Gnome desktop and selecting new terminal or by clicking the redhat menu, highlighting system tools and choosing terminal.
Now you need to get into that new directory it created. Use the cd command like the old DOS terminals...for instance if the new directory is in your "home" folder, you will type
and watch it install. It will prompt you for a few things (do you want to install the windows-free version, your root password, do you want to install wine, etc). Note that you have to type "yes" or "no", not just "y" or "n".
It will tell you to go rent a movie or do wash and come back in a while. Check back and answer any more questions it has. You do want to have it install the required "fake drive" directories for you, and also you want it to copy the .reg and .config files, when it asks.
Now when it's done and you want to use wine to run a program (let's say notepad), open a terminal window and type
or setup off of a CD, wine d:\\setup.exe
Hope this helps...it all isn't as straightforward as you might think for us newbies :-) It's not too bad though.