If you look in the library folder you find a file named README.md, which contains, among other helpful information, this:
How do I get set up?
- Please refer to the project's wiki
So that is a bit helpful.
You also may notice that folder contains some files that start with "doxygen". doxygen is a tool that automatically generated documentation from comments in the source code. So that's a clue that somewhere in the folder structure you will probably find the generated documentation. Sure enough, with some digging we find LiquidCrystal_I2C/utility/docs/html. Open the file LiquidCrystal_I2C/utility/docs/html/index.html and the complete documentation will open in your browser. The most useful content is found under the Classes tab.
As J-M-L said, you also can find a lot of example sketches in the Arduino IDE at File > Examples > LiquidCrystal_I2C.
So that's the specific answer but the general answer is that it's going to be different with every library. The only thing you are sure of is the source files. Sometimes you will find information in the comments in the source code that lead you to a website with more information. Some will put documentation in the README.md (or similar) file. Some will put it in a wiki, often times which is not mentioned anywhere in the readme, you just have to find the library's repository and click the Wiki tab. Some use doxygen. Some don't bother with any documentation at all. You just have to put on your Sherlock Holmes hat and do some sleuthing. Luckily in this case there was plenty of information included with the library but sometimes that is not the case and when there are multiple libraries of the same name that get confusing because you need to figure out which of the libraries it is. Ideally the place you downloaded the library from would provide that information but you'll find things like this Instructable where they don't bother to provide any information about where they got the library from. If you installed the library using the Arduino IDE Library Manager (Sketch > Include library > Manage Libraries...) you will usually notice a "More info" link in the library entry that may lead to information.