Yesterday I gave a talk on Determinacy at the Graduate Student Seminar here at BSU, and just posted the slides in my talks page. I also posted the slides of the previous talk I gave at the seminar, two years ago, on Very large finite numbers.
The talk tries to avoid as many technicalities as possible, and presents the infinite games that set theorists are mostly interested in within the larger context of game theory. (I did not mention long games.)