The MuseScore apps for iOS, Android, and Kindle Fire devices let you connect to your account on MuseScore.com, and play, transpose, and view individual parts from your scores as well as scores shared by the MuseScore community.
There are two versions of the app: the free MuseScore, and the paid MuseScore Songbook. The free app only allows you to access scores that are online on MuseScore.com; Songbook also allows you open MSCZ files from your device's local storage, email, or Dropbox, and download scores to save for later.
After installing the app, use it log in to your MuseScore account. The app's Discover view shows recently uploaded scores. To access your own scores and favorites, go to My Scores via the hamburger menu in the top left corner.
When viewing a score, standard Play and Rewind buttons appear at the bottom left. When viewing or playing any score, the ⋮ icon in the top right corner exposes the Download, Favorite, and Share buttons. The loop button to the left of the bottom middle lets you set start and end measures to loop between; the magnifying glass icon lets you change the note size of the score.
Take the video tour to learn about all functionality in the app.