It's not necessary to read academic articles in order. In fact, because they are well-organized with each section serving a different purpose, it's recommended that you read a scholarly article in the following order:
Abstract = always read the abstract first!
The short summary is listed first, below the title and author information, and it gives you an overall picture of the article's purpose and findings. It will also tell you if the article is relevant to your research interests.
Discussion / conclusion = skip to the end!
The discussion or conclusion section tells you what the authors actually found. This gives you a better sense of the results of the original research or experiment the authors were exploring.
Introduction = what the authors hoped they would find (hypothesis)
This section will tell you what you about the authors' hypothesis or research focus.
If you have time, you can read the following sections for specifics:
Literature Review = what other scholars have said about the topic.
What are the agreements or disagreements in the field? What part of the topic has been under-researched and needs more study?
Results = the specifics of what the authors found
Look at the data for yourself! Does it match what the authors said they found in their discussion?
Methods / Methodology = how the authors evaluated their hypothesis
How was the experiment designed? What did the authors choose to include or disregard?
Don't forget the References section!
It's tempting to skip the last few pages of an article, where the authors have listed all of their citations (i.e. the bibliography or reference section). But if you find that an article is useful to your topic, you can find other relevant articles by seeing the sources the authors consulted themselves. Once you find a citation that looks interesting to you, contact your Faculty Librarian or search Google Scholar to see if the article is readily available.