Dominic, it is pretty simple to connect, but first you have to have the game loaded on your PC. You talk about downloading Counterstrike 1.6. For starters it helps to have a legal version of the game in your cupboard. Most of these games will authenticate with the manufacturers server. Once you have authenticated, then you get the option to join a game playing server. Here you will normal see thousands of games been played all over the world, doesn't help much as we can't play overseas with a 400ms ping time. So you have to look for the local servers. That link to saix is great, from the list of servers that you can obtain there, you now enter one of these in the option of the game which says you can enter IP address manually. If it is right, game details will come up. You should be able to tell if it is clan, locked, etc. by icons used. By clicking on this you will then be able to join.
On Saix there is a nice UNREAL 2004 demo which you can download. You can connect without having the real version but don't forget to get the IP address from saix. This will give you an idea about online gaming and will be the start of about a thousands other things that you will have to learn about, ie. lag, ping latency,cheats and will so occupy your time that you will never see the sun again.