How To Create A Video In Video (Picture in Picture) In DaVinci Resolve
Synchronizing the clips and creating a picture in picture effect are really two separate issues, and you could take many approaches to each.  But basically, you drop one clip on one video track, and the other on a different video track.  You synchronize one to the other by dragging either clip left or right on the timeline until they match temporally.  There are automated approaches to this step, including timecode-based sync and audio waveform based sync.  These automated processes are described by the manual in detail, but they essentially perform the same function as manually aligning the clips.
Once the clips are aligned temporally, you can apply a picture-in-picture effect by spatially shrinking or cropping the &quot;topmost&quot; clip (the one with the higher V#).  You'd do this by clicking on the clip in the timeline to select it, then altering its zoom, crop, and position controls in the inspector tab.  Alternatively, you can use GUI transform controls by clicking the transform control button at the bottom of the program monitor, then using the onscreen controls.
This is a very barebones explanation, and one which will work in many older versions of Resolve.  There are fancier approaches, ones which involve the Color Page, or the Fusion Page, or (beginning with R17 beta) ones which use the &quot;Video Collage&quot; ResolveFX.  These are essentially variations on the same basic premise.  The Collage effect does offer many handy shortcuts to produce rounded corers, drop shadows, borders, and animated transitions, as well as re-framing, keyframing, and handling stacks of various tile arrangements, so I would recommend trying the R17 beta if that's an option, for the sake of convenience.