Without the Paypal Sandbox you would have to place a real order from another credit card or Paypal account to test the transaction. It is much easier to set up your test accounts and test your sites in the test environment - where no money changes hands.
Well - today is your lucky day! I have put together a video series that shows you how to prepare your site and set up and use the Paypal sandbox for Website Payments Standard. You can be testing your own sites in the next thirty minutes.
You will see how to use it in simple situations (like taking a payment and routing to a download page upon successful payment). I will also show you how to integrate Paypal's advanced features for use in scripts like membership scripts. (Specifically S2member, but the process is the same for other scripts).