Well, I'll try to give some examples without being too specific.
Basically the document explains Google's various advanced syntaxes and ways you can use them to get access to thing you really shouldn't have access to. These are all things that are just unsecured and are accessible anyway, it just helps you find them. It surprised me how many people had these types of things exposed with no type of security.
A few examples:
There is a certain syntax and query you can use to find exposed bash_history files, which, according to the article sometimes have encrypted unix passwords hashes in them and also tells you how to crack them.
Most of them are just ways to search for open indexes and certain files in them. There is also certain syntaxes to use to find vulnerable windows servers that have, for example, the system32 open to the public. I tried this syntax and the first result actually had that folder unsecured and also the cmd.exe unsecured.
I could send this document to a moderator and have them check it over to see if it is postable, or maybe takes some parts out of it. I really don't think it would be approved though because it is VERY specific about these hacking methods.
Edit: I tried clicking on the cmd.exe because I know that I couldn't really do any damage just clciking it in IE, it would just try to download it. Well I got a 403 error so maybe it's not as unsecure as I thought. It is still alarming to find that directory has index enabled though.