First, check to see which banks are offering competitive high-yield savings accounts. Once you find one, the process is easy, online or in person. It will be especially easy if you open an account online with a bank you already do business with. It has already verified your identity. If you're opening a savings account at an institution you haven't worked with before, there might be a few more steps. You'll need your driver's license, Social Security number, and primary bank account information at hand for the application process.