Practicing your dancing beforehand might help you avoid embarrassment later and make you a bit more comfortable once you get to the club. Dance in front of a mirror and take note of how you look. Don't try too hard, just turn on some music and move how you feel.
Relaxing is key to enjoying yourself while dancing. Don't allow negative thoughts to enter your mind, and don't envision yourself being embarrassed while dancing. Just go out and do it without thinking about. Have a drink beforehand if you want to help you relax, but don't have too much, or you're guaranteed embarrassment.
Don't use a lot of excessive movement; keep your hands and feet movement to a minimum. Just let your body "groove" to the music. Try dancing alongside a friend and mimic their moves, perhaps even striking up a conversation while dancing to keep yourself from over-thinking your dancing. Moving your limbs too much not only looks ridiculous, it may also cause you to bump into someone else, which is much more embarrassing than a bad dance step or two.
Dance on the edges of a group of people. If you're dancing in the center, you'll also be the center of attention and may stand out from other people who are dancing a lot more than you. Stay on the edges where people are just grooving, having a drink and talking, and you'll be more likely to blend in to the surrounding environment.