I need to create a script that will log into an authenticated page and download a pdf. 
However, the pdf that I need to download is not at a URL, but it is generated upon clicking on a specific input button on the page. When I check the HTML source, it only gives me the url of the button graphic and some obscure name of the button input, and action=".".
In addition, both the url where the button is and the form name is obscured, for example:

url = /WebObjects/MyStore.woa/wo/5.2.0.5.7.3
input name = 0.0.5.7.1.1.11.19.1.13.13.1.1

How would I log into the page, 'click' that button, and download the pdf file within a script?
You could observe what requests are made when you click the button (using Firebug in Firefox or Developer Tools in Chrome). You may then be able to request the PDF directly.
It's difficult to help without seeing the page in question.
Advanced screen-scraping using curl