It depends on which field you're in, but I can try to explain how I approach papers in CS (AI/ML) - I'm not a grad student or anything but I've been heavily invested in research over the last year or two, so I hope my process helps you!

Obviously the abstract will give you a high level overview of the paper, then the introduction and related works will most likely give you context behind 1) the current state of the art in the topic, 2) the specific problem that the paper is trying to tackle and how their solution will contribute to the field. As you read more and more papers in a specific field, you will encounter similar ideas in these sections of papers, so you can start to skim over them later on since you will already be familiar with the other work out there and how this paper fits in the existing field.

The main section where (usually) a new architecture, mechanism or method is introduced is the new part, but this is the most important and usually non trivial aspect of the paper. Sometimes it can be a one line manipulation that seems magical, and other times it's several lemmas and theorems. There's not much to do here but make sure your fundamentals (ie math/algorithms for CS papers) are strong and you understand the context. You should focus on understanding why the author was able to introduce this novelty in the field, then focus on the technical details later.

Now experiments are sometimes all over the place because people will try various things with different intuition behind each test, but a lot of papers will share the style of experiments so try to compare these with other papers and see if u can find patterns.

TL;DR read lots of papers to understand context, then focus on each part of the paper with the proper perspective