Play on the new Deathmatch gamemode in a PvP battle arena. (Best with 8-16 players!)
Download the client.
Once downloaded, extract everything to your "steamapps/sourcemods" directory. You should now have "steamapps/sourcemods/tf2classic".
3. Install Source SDK Base
Go to the 'Tools' section in your Steam client and Install Source SDK 2013 Base Multiplayer.
4. Restart Steam
Once it has finished updating, restart Steam
Check your games. You should see "Team Fortress 2 Classic" has appeared on your games library.