Research
Some of the things to avoid are:
Companies offering to sell you lists of drop shippers for $3, $4, $7. The old saying "You get what you pay for" applies here. Spend $4 on a drop shipping list, and you'll get an e-mail listing 200 company names, addresses and maybe phone numbers. A few calls to out-of-service numbers, and you'll realize that the list is years old and basically useless.
Companies charging you a "monthly fee" to be your drop shipper. Think about it: Why would a company charge you to sell you things? Answer: Because their products are either worthless junk or they're marked up way too high. In either case, they know your online store won't be able to sell any of them, so they need to make their money from you through a monthly fee.
Companies offering you a turnkey online business, complete with Web site, products that can only be purchased from them), and a merchant account that allows you to accept credit cards. The strategy here is to get you to spend your money advertising and selling their products that they're buying from real wholesalers, marking up and selling to you. These companies usually also charge a one-time and/or monthly fee.