First, you check Wikipedia. Going to https://en.wikipedia.org/wiki/Perfect_graph and clicking on "Families of graphs that are perfect" gives you a list that includes comparability graphs, and a citation for the list: West's Introduction to Graph Theory.
Then, you look in that textbook. The index tells us that comparability graphs are mentioned on pages 228, 231, and 329-31, with a definition on page 228. Two paragraphs down from the definition, we have
5.3.25.* Proposition. (Berge ) Comparability graphs are perfect.
The proposition is followed by a short proof. It would often be acceptable to cite the textbook for this fact (as Wikipedia does), especially if you're citing the textbook for multiple facts, but in this case, we have more information: we can go to Appendix F: References and see the citation
Berge C., Les problèmes de coloration en théorie des graphes. Publ. Inst. Statist.
Univ. Paris 9 (1960), 123-160.
And now you have the original source.
A note on consulting a source before you cite it: Wikipedia is not always reliable, so I would not claim that the theorem is proved in West's Introduction to Graph Theory before actually checking what the textbook says. However, West is always reliable, so I would be fine citing the paper above even if you haven't read it, or don't know French.
If you want to be more careful, you should cite the textbook, and mention that it attributes the result to Claude Berge in such-and-such paper. Or, you could read the paper and find the proof there, in which case you're safe - but should still cite both the textbook and the paper, because the textbook might be easier for readers to find.