MuseScore -- Index -- Slurs

select first note:
<S> creates a slur
in edit mode:
<Shift+Right> moves the slur
end to the next note:
<X> flips the slur direction:
<Escape> ends edit mode:

A slur can span several systems and pages. Slur start and end is anchord to a note/chord or rest. This means that if the notes move in a relayout, the slur moves to.

See also Ties, Edit Mode.