Wow, the old TF mod for Quake...
My first suggestion would be to hit up planetfortress - http://www.planetfortress.com/teamfortress/download.html
You'll want to download the Team Fortress 2.8 version for clients, not the server install.
There are also map packs you can download a bit further down the screen that will let you get all the maps currently available for TF.
There should be a readme file in the client download that will tell you were to unpack the files. It's been years since I've played, due to loss of interest by the community and very few servers still running the mod besides bots, but I believe you create a folder called fortress in your quake directory and unzip the files there.
You'll want to create a new shortcut with the following command line: quake.exe -fortress. "fortress" would be replaced with whatever folder name the readme file tells you to put the files in.
Also, what Windows OS are you attempting to run Quake on? I had initial problems loading on Windows 2000, Vista and 7 because Quake does not natively support the NT environment. My suggestion would be to check out http://quakeone.com/forums/quake-help/general-help/173-windows-xp-quake.html.
They have a link to a copy of ProQuake designed to run on newer operating systems. I couldn't even get the game to unpack on windows 2000 because of the NT environment, but there should be plenty of work arounds out there if you search Google and some of the old Quake forums.
You can also run the single player TF, but it is no where near as fun as it was back in the old days. A quick shout out to [KiN]