First an answer that is (half) joking. Try to read the paper. If that fails your understanding, get the papers cited in the references and try to read those. Proceed recursively deeper until either (a) you understand the paper(s) or (b) you reach Euclid. In case of (b) you should probably find another field. In case of (a) work forward again to the original paper.
While there is some truth to the above, appalling as it sounds, note that the farther you go back the broader is the coverage of the papers, generally speaking. The research frontier (where the professor wrote the paper) is very narrow in mathematics. But it has a lot of background that goes into getting to that frontier. If you understand that background, or at least some of it, you are doing well. The research edge is like the tip of a funnel, with a wider body of knowledge behind it. Textbooks stand a fair ways back from the frontier, but maybe a bit closer to the edge than they are to Euclid. If you have a good general understanding of the broader field (analysis, say, or algebra) you won't have to go back too far.
I'll note that this is much easier to do now than it was fifty years ago. Then, to trace back a chain of citations you had to go to a physical library and for many of the papers ask the librarian to get you a copy from some, yet bigger, library. Now, the more recent stuff is available online, though you may still need to have the librarian get you a copy to avoid charges imposed by publishers.
It is a hard job to get started in this. Having done it once, however, for a narrow field, the outlines of what is known in that sub-domain will become clearer to you and you won't need to repeat this too often. Moreover, the funnel narrows fairly quickly so there is, perhaps, less to understand than you might fear.
In my own case, the number of steps back from the edge to what you could find in good analysis textbooks was only half a dozen steps, if you had the right insights. The essential papers you needed to read to get the insight was, again, only half a dozen or so. With those insights I can explain the essence of my work (very old now) to good undergraduates, though not with all the details. OTOH, it is probably the professor him/herself that will give you those insights.