How to check if floor is level
The common tool to do this is a level. One that is 4 feet long is better because it can check the floor over a wider area for flatness and level. You really only need to check the area where you intend to set the book shelf and not the whole room.



A level like this would not be considered an advanced tool as they are rather simple devices. If you find the longer sized levels too expensive you can instead find cheap short ones that you can use on the top edge of a 4 foot long, straight and even pine board.



If you want to avoid buying any tool at all you could consider the idea to use pine board like the above example but substitute the cheap level with a Smart Phone running an app that simulates the bubble style level. For example there are many apps like this in the Google Play store for Android phones. (Similar apps on iPhone at the iTunes store site).

 

The smart phone apps require you to calibrate your phone on a known level surface. Some folks may consider this idea a gimmick but it may be just what you need for a quick and simple check. The quality and repeatability of the cell phone type of app can vary from app to app and be affected by the quality of sensors in the phone. So if you go this direction I encourage you to download three or four of the free apps and find the one that best suits your needs.