I am trying to create an ASP.NET page that connects to QuickBooks Online Edition, read a couple of values, and display the results. So far I have downloaded the QuickBooks
The outline of what you have to do are outlined in Chapter 7 of the QBSDK documentation (at least in the 7.0 version of the SDK that I have). You have to open a test account and get permission to connect to their servers.
Once you have your account setup, the basic authentication procedure consists of redirecting your user to the QuickBooks Online site to log in, and once the user has done that, QuickBooks calls back your application with an HTTPS post with a ticket, which is basically a session handle that you can use for your requests, so that the system knows you are authenticated. When you get that response, you parse it and send your own login request to the system based on what you got back.
Then (if I understood the documentation correctly) you are basically doing Https POSTS of xml files with the QuickBooks requests, and you get XML responses that you have to parse to get the data you want.
I hope that gets you started.
The rest of the SDK is documentation (which you will need to know how to form your requests and parse your responses) and everything else is concerned with how to communicate with the desktop product. The only thing you are going to need from the rest of the documentation is how to do error handling, which is really only important if you are posting data to QuickBooks. If you are just reading, it doesn't matter (either your request works out or it doesn't, you don't need to worry about if you need to retry or if that would result in duplicate data).
EDIT: Given your specific use case I see two options. (You aren't crazy, just not the typical QuickBooks Online scenario).
One is to programatically hit up their login page and submit the credentials as if you were a user. I'm sure its not "supported" but it would likely work.
The other is to cache the results (which you should probably do anyway) and have an admin screen where someone does log into QuickBooks online and update the results every morning or evening or whatever makes sense.
In most small businesses, they are going to opt for the first option, but the second one is going to work more consistently, robustly and actually be supported by Intuit if you have an issue.