Find a vendor with a large selection of ballroom shoes. You'll likely find one at ballroom events such as dance competitions.
Bring the outfit you're going to wear with the shoes. You may want to try them on together to see how they look.
Consider the dance you're doing in them. Men's shoes are often simply just Oxford style shoes, while women's shoes can come in a variety, according to dance, or standard (closed toed heels that are about 2 to 2.5 inches with an ankle strap and a bit of a flared heel) shoes. Standard shoes may be worn in several dances, while Latin dances typically favor an open toe shoe with a higher heel.
Consider the color. Tan shoes go with almost any costume and elongate the leg. Look at the construction of the shoe, as well. Make sure it is well made without strings hanging off or sharp edges that could potentially slice into you or your partner. Take closed toed and open toed shoes into consideration, as well. Open toed can look flashier, but do not protect your feet against the elements as well.
Try them out on a dance surface or hardwood floor before purchase. You will want your dance shoe to have enough grip so that you don't take a spill on the dance floor, but enough give so that you can execute moves with ease.
Make sure the shoes fit you snugly, but do not pinch.
Consider purchasing arch supports for high heels or flats (men or women) to ensure your feet will not be more prone to injury during dancing.
Make sure the shoes are lightweight as heavier shoes can be a hindrance to more complex moves. Your shoes should also be no taller than 3 inches for women or 1.5 inches for men.