Standard text editing shortcuts work fine:

Ctrl+C Copy
Ctrl+X Cut
Ctrl+V Paste
Ctrl+Z Undo
Ctrl+Y Redo
Ctrl+F Find

Hit Ctrl + Space to open a contextual menu with suggestions from your current code and your current language:

And if you’re editing a plain text file, you can still get suggestions for all the words contained within the document. (From news post What we’ll find in Notepadqq 0.40.0)

Select a block of columns from multiple lines at the one time for cutting, copying, pasting, typing or deleting text:
Alt+Shift

As illustrated here, from overview page:
(Click to view in better quality.)

Same as above, but with multiple blocks of columns:
Ctrl+Alt+Shift

Find a text pattern, then overwrite it with different text or add more strings of text before or after:
Ctrl+F, enter string, then "Select All" button

For example, Ctrl+F and search for "trees", click the "Select All" button, then type "forests" to replace all instances of "trees" with "forests"

Further shortcuts can be viewed and set in Settings -> Preferences -> Shortcuts