I'm wondering if there is a quick and easy way to synchronize a video of a conference speaker with the slides that the speaker shows without having to manually edit them in Premiere or Final Cut. The result should look something like this: https://youtu.be/o12-90Dm-Qs?t=699 Also I want to avoid another camera just to record the presentation.
Without having to do anything? No, that's probably impossible. How would the computer know when to switch to the next slide? What you could to is capture a video of the screen of the computer used to show the presentation using some software like fraps and synchronize the screen capture and the camera recording. However, this has two downsides; screen capture software tends to produce very large video files, which could fill up a the hard-drive of a normal laptop really quick. Also, your video quality would be far from perfect.
What I would probably do to minimize working hourse is capture a small (i.e. SD) version of the presentation and use that to insert the slides manually in Premiere (or whatever you're using). If you have the screen capture as an indicator as to when each slide was shown, inserting the original ones in another video track at the right times should be a matter of minutes ...