EBay
EBay remains the go-to place for selling sports cards: granting you access to a worldwide audience and providing a fair-minded middleman to help complete the sale. You simply post your cards on the site, set a given closing date and wait to see who nibbles. Ebay recommends selling common cards in bulk, which tends to get you more than you would if you sold them individually. (Rare or valuable cards can be sold by themselves more readily.) In addition to providing a great forum for selling, eBay also helps you gauge the going price for basketball cards; you simply search for identical cards for sale and check the bid amounts to get an idea of what your collection is worth.
Other Websites
The Internet is full of websites, such as Sportsbuy.com and Sports Card Depot, that allow you to sell your basketball cards. Specifics vary by site, but they usually use a system similar to eBay: introducing you to prospective buyers, allowing you to advertise your cards and serving as a broker for the sale in some cases. Some websites may collect a commission for successful sales or require membership to avoid swindlers and cheats. The benefit of such sites is that they attract precisely the sort of people interested in buying basketball cards, reducing the legwork required to find a customer.
Local Stores
Local stores are more difficult than websites because you're beholden to the needs of the particular store owner. They usually only take rare cards worth a fair amount of money, and they usually look to lowball the price in order to turn around and sell it for a profit. This can be problematic for basketball cards, which usually aren't worth as much as baseball or football cards. The benefit is that you can sell your cards fairly quickly and don't have to worry about shipping costs the way you would if you were selling online. If none of the stores in your local area will buy your cards, look for a collectibles convention or sports convention; hundreds take place across the United States every year. The dealer's room of such conventions likely has a large number of store owners and other buyers willing to purchase your collection.