Visit the websites of well-known, established banks. Some examples of banks with strong, positive reputations are Bank of America, Citibank and ING (see Resources). Avoid credit unions. Because credit unions are member owned, they always require an initial deposit, without exception.
Research each bank's policies, interest rates and rules regarding withdrawals, checks and deposits. If you are researching several banks, make a spread sheet, indicating each banks fees, interest rates and perks. If it will make you feel more confident in your decision, use a site like www.bankrate.com, which offers independent ratings of many banks in the United States.
Choose the bank that best fits your needs. For instance, determine if you'll be given a debit card or if there are local branches in your area.
Fill out the bank's required applications online. You'll need your Social Security Number, driver's license number, a mailing address, phone number and employment information. In most cases, you'll also need the name and number of a friend or family member who does not live with you.
Check the application thoroughly before submitting it. Any mistakes, typographical errors or missing information can slow down your approval process. Most important, make sure that you include the correct email address, so the banking institution can contact you when it approves your application.
Wait the necessary amount of time to be approved by the online bank. This can take anywhere from a few minutes to several days. Check your email often, just in case the bank sends you an email requesting more information.
Make note of your new bank account number after you've been approved. Although you were able to open the bank account online with no deposit required, chances are you'll want to make deposits to the account in the future, and having this account number in a secure place is a good idea.