This walkthrough from Mastering.com's Logic Pro course covers several ways to clean up edits with fades and crossfades, all aimed at killing the clicks and pops that show up when audio gets chopped up.
The fastest method uses Logic's fade tool click zones: hover over a region's corner to drag a fade, or grab the adjacent handle to shape the curve.
For crossfading between adjacent regions, the key command Control-Option-X applies one instantly, without manual dragging every time you edit.
Most edit-point crossfades only need to be 6 to 10 milliseconds. Logic's default is set to 20ms, so adjusting that preference down saves cleanup work on every future edit.