I have my db set up as one record is an expenses(invoice or credit card purchase) and I have a container field that holds the pdf of the invoice or credit card receipt.

The user will be accessing this db through the internet. I have it set up when the user opens the pdf file, it is saved to their desk top. Is there ANY other way I can have the user open a pdf file without having to save to their local computer?

Please advise.

Sure, what you should do is to use the open URL script step and set the URL to http://yourserver.dom/somefolder/yourpdffile.pdf

The URL will then open in Safari/Internet explorer, and provided they have Acrobat (or some other PDF viewer) installed in their browser the PDF will open and display inside their browser window.