Run steam. Go to the "play games" window. Click "browse games".
Then click "register product i already own" and register the games you have and let it do its thing (might take a little while to do all the updates). And after all of that is done, go to the "individual games" tab and look for Counterstrike and click "play game". It will download and update and you should be ready to go!
Its really fun to browse through all the games on the game browser. The 3rd party section has some great mods