How to read a research paper with too many references to previous works?
What you are describing is pretty normal in academia. People take on old and existing work, and build upon it. 

There are typically several reasons for citing prior studies, thus the impact of each individual citation might (and usually does) vary as well. I reckon this is all quite new to you. In your case if you can understand the work presented in the paper without diving into the citations, then just do that and ignore the references for the time being. You can always trace back to specific (read: not all) references later on to fill in any potential gaps in your understanding.

If you cannot grasp the why or the how, then my suggestion is to pay more attention to the introduction section, checking out the important (often recurring) references, and then re-reading the introduction. You should get a fairly good idea of what the paper is really about this way.

Another approach could be to try to discuss the paper with your supervisor or someone else who might be able to judge it better (any grad students or TAs?)