The key reason for refining your palate is to aide in picking up the subtilties in your smokes, so here are a few tips that I believe will help you out:
1.) A "refined" palate doesn't come over night and isn't available to everyone. Genetics has a lot to do with it as well, so don't get discouraged. The main key is to try a WIDE variety of cigars and to concentrate on them when smoking. (ie: Don't be working on your car or mowing your lawn.)
2.) Smoke slower! Remember the one minute rule between draws. This is the most common reason people don't pick up certain flavors. For one, they smoke too fast which causes a cigar to get hot and bitter. Secondly, because they are smoking to quickly, they don't have a chance to savor the flavors and don't concentrate on them. Try it, I guarantee you will pick up more flavor.
3.) After taking a draw and expelling the smoke, take some air in through your nose and mouth (at the same time if you can do it). By drawing air through you mouth and nose you pull some concentrated flavors across your olfactory and can usually pick up a ton of subtle flavors this way.
6.) Smoke a cigar that has been reviewed and try to follow along with the reviewer. You'll be amazed at how smoking along with someone else's notes will help you pick up flavors that you couldn't put your finger on.
7.) Take notes for yourself! Break the cigar down into thirds (first 1/3, second 1/3, final 1/3). Most cigars change flavor in these areas so it's a good general rule to follow. By taking your own notes, you slow down and concentrate on the flavors.
Hope this helps and happy smoking my friends!
~Mark