Simply enter into any tournament inside the CC. These are difference from the Xbox Live tournaments. If you are the owner of the CC simply create a CC tournament. If your a member, the leader more than likely already created some. If not ask the leader to create a few tournaments. As with most of the other online achievements once you start the round the achievement will unlock and you do not need to finish if you like.
To create a CC tournament:
First you have to be a GM in your club. If not ask the GM to do this so you at least get some tournies going and you get your achievement for playing in one. Simply go to easports.com, hit the Tiger Woods link, sign in to the site and hit the Country Clubs tab. In there you can create daily, and weekly tournies for your club.