MuseScore -- Index -- Slurs

select first note: First note selected
S creates a slur
in edit mode :
Slur to adjacent note
Shift + Right moves the slur
end to the next note:
Three-note slur
X flips the slur direction: Slur above note stems
Escape ends edit mode : Slur no longer in edit mode

A slur can span several systems and pages. Slur start and end is anchored 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.