I'm giving a talk summarizing someone else's paper and I'd like to show some figures from their paper during my presentation. It's an informal talk to fellow students and a few professors at my school. Would it okay to just have a PDF of their paper up on the screen showing the figures needed? Should I obtain permission before I do this?
In my field, mathematical physics, I've seen many presentations with figures from papers, and it's perfectly acceptable to do so providing you reference the work either at the end on a separate slide or as a footnote.
If the figure does not consist of data collected by the authors, but rather, for example, the graph of a function, then you could of course plot it yourself and include your own figure. There would be no need for citation.
The thesis writing guide of Tampere University of Technology (Thesis Writing Guide at Tampere University of Technology, p. 35. March 2014.) says the following about using figures from other sources in your thesis. As the theses are published, I believe the following applies also to presentations:
If a table or figure is cited from another volume [i.e. published paper], the in-text citation is placed in the caption or the heading of the table. The full reference is listed at the end of your thesis.
If you edit a figure or table taken from another source, for example, to ensure that colours, terms and notations match the rest of your thesis, you add ”adapted from ” to the citation.
These recommendations are legal at least in Finland. Even though we have quite similar copyright system with the other western countries, your local system might differ.