How I read Mathematics. First try to find the paper. First use http://front.math.ucdavis.edu . If you can't find it then use google scholar. If that fails then go on the authors academic website. If that fails then see if the author is live and try to contact them. Then repeat for their grad students. If all else fails post it to r/math or HN and ask for the pdf.

First you want to see if this paper is even worth reading. Scan the Abstract and the conclusions. If it is still relevant then do a quick scan of the whole text and look for the things you don't understand. For everything you don't understand look up on wikipedia. Once you have found those pages then look on the citations on wikipedia to gain more understanding. If you still can't understand the paper reread it and then attempt to redo their calculations. If all else fails ask someone to help you read it. Whenever you get confused write on the paper questions. If you figure out that this paper is meaningless then look for another one.

If you figure out a new question that you want to persue more then try to answer that question. If you don't have access to professor or if they are impeding your work then use stackexchange. Either that or try to invalidate your new theory yourself. Recognize that you can be wrong.