Menu: Edit -> Copy
Accelerator: Ctrl + C
Toolbar: 
Drag and drop: see below
Copy copies the selected logmessages or the selected logfilter or subfilter (including its subfilters) to the clipboard.
If a copied logfilter contains references to other logfilters these logfilters will be copied to the clipboard as empty filters.
Using drag and drop for copy and paste:
For copy and paste you can also drag a filter / subfilter and drop it over another filter / subfilter while pressing the Ctrl key.