Learning how to dance together is the most romantic, entertaining, fun activity you will ever do together. Its not hard, and the return on the investment of a few hours of your time is a lifetime of pleasure. The "First Dance" has become a pivotal part of most weddings. You don't want to look silly, or have it be boring, but you also don't have a lot of time, and of course cost is, naturally, a factor. Still, try to make learning how to dance together an opportunity, not a chore!
First: relax, don't worry. If you can walk, you can dance.
Next, if you have a special song that you want to use on the Big Day, great; work with someone to decide what the best style of dance is for that song. If you don't have a specific, special song, it won't be a problem, and great dance songs are everywhere you look. Just take a little time. Most dance instructors suggest giving yourself six months. That doesn't necessarily mean they are saying you need to take two lessons a week for half a year to do one dance(!), but rather that starting six months before the wedding will give you ample time to,
a) check out the options available to you,
b) comfortably learn how to move together, without feeling pressured and under the gun those last few weeks before the wedding - when you will be juggling a thousand other last minute things.
Wherever you are located, there are lots of options for learning how to dance, but choosing a quality Dance Studio or instructor does take a little research and some common sense. The internet makes the research part easier, but don't overlook various other local listings, referrals from friends, or flyers and/or cards at your other wedding vendors' locations. Also if you are shopping around looking for the cheapest thing you can find, keep in mind that you generally do get what you pay for - you may learn how to do a few steps, but you might not be learning how to dance, and people will be able to tell the difference. It won't be much fun to do, and haven't you been to weddings and watched the couple move like wooden automations while they danced? Yes, sure they learned the dance, but they didn't learn How to Dance together, as one. Married life is hopefully going to be a long and wonderful dance through the years together, giving and taking, leading and following. If you can, make that First Dance a perfect symbol and springboard for your future together.
One of the things I have noted in the past is that students work best when they are comfortable and relaxed, so be sure that you actually like your instructor! That should be the first thing you decide. Take advantage of Trial lesson offers, introductory lessons which are either low cost or free. (But be prepared for the interview afterward, when the instructor or studio presents their comments, recommendations, and of course the Pitch. After all, the Studio does want you to take lessons - it has to, to stay in business. But do not let a Hard Sell trap you - if the studio has to resort to Used-car-salesman techniques, it may not have a lot of confidence in its instructors.)
Look for atmosphere. Are people friendly? And is the Studio clean?
When you are dancing, remember to always have fun. That's the most important thing. Learning a dance and its specific steps and rhythm patterns are just tools you use to make the dancing (the communication between two bodies) easier. But it is your First Dance! Remember to keep it stress-free so that you can enjoy it!