Use one of the above methods to download the game, I recommend using the Installer (MSI) files, and then run though that.
Once installed, run the launcher from the directory you installed it to, and this will start updating the game.
Once it has updated to the latest version (Currently: 5.24) You should see a list of servers in the launcher. It will also tell you how many players are playing on that server along with other details.
Just click "Join Server" and the game should load.
If you happen to need any of the maps on the server, the launcher should try to download them for you, so it may take a short while to download (Dependant on your download speed).