First, you'll need an account.  Hit the DigitalOcean home page and click that SIGN UP button.

You'll want to pick a good password here, since access to this account gives root access to the servers you host under it.

Next, check your e-mail for a confirmation message from DigitalOcean, and click the confirmation link inside.

You should then be asked to provide a credit card number to pay for the account.