Hi there, depending on your set up this may be a long answer!
Have you got steam installed? If not then the first port of call is to install STEAM.
http://store.steampowered.com/about/
Instantly access your favorite games
Over 1,100 games are available to purchase, download, and play from any computer. Check out the new releases, indie hits, casual favorites and everything in between.
To install this,
Ensure that you are logged in as an administrator on the machine which you would like to install Steam on
If you have previously installed Steam and are reinstalling to remedy a problem with your prior installation, please see the Uninstalling Steam topic for instructions to remove any prior Steam installations
Check the Troubleshooting Network Connectivity topic to ensure the required ports for Steam are open on your network
Download and run the Steam Installer from Steampowered.com
Or covered here for PC :
[youtube]
http://www.youtube.com/watch?v=w0hJrn5Z ... r_embedded[/youtube]
Or here for Mac:
[youtube]
http://www.youtube.com/watch?v=cKY41oC1 ... r_embedded[/youtube]
Once that is installed, you will need to create a steam account; here
https://store.steampowered.com/join/
(Be sure to remember your password for when you log on

)
Now you are all set up and ready to go! Well, nearly...
Open up steam, log in with your account which you just made and then head on over to
http://store.steampowered.com/app/440/
Time to part with that hard earned cash!
Add items to your shopping cart
Once you're ready, visit your cart (by clicking the green link in the upper right hand corner) and checkout by selecting either "Purchase for myself" or "Purchase as a gift."
Log in to your Steam account
Continue through the checkout process to complete your transaction on Steam
The game will then begin to download, as if by magic!
Time to get down to the nitty gritty of waiting. While you do this, you may wish to go for a run, have a coffee, catch up with glee, we have some time to kill so go off and I'll wait for you here.
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Ah, welcome back, Tf2 has just finished downloading and we are ready to begin browsing for servers!
Now on our homepage you may see a little widget to the right with the server address below it; without a server 1 name tag, you may get a bit confused; but never fear because we are here to help. Give this a read through and decide on the correct server for you!
http://forum.specialattack.net/viewtopi ... =74&t=9795
Now, back to the homepage at
http://www.specialattack.net, you can see the list to the right, and it is as easy as a cheeky left click and join game! This will launch team fortress 2 for you, and you are ready for all the action!
If you need any tips on how to play in the game, there is a very informative article with many links here:
http://forum.specialattack.net/viewtopi ... =74&t=9738
Have fun, and happy hunting!