Tap a piece on the Music tab to download and open it as a PDF, in whichever app your phone normally uses for PDFs.
The first time you open a piece it's downloaded fresh; after that, Mozzy keeps a local copy so you can reopen it instantly — including with no signal, e.g. backstage before a concert. If the file on the website is ever replaced (a corrected part, for instance), the next tap fetches the updated version automatically.
These local copies do use storage on your phone over time. See Clearing cached sheet music to free that up whenever you like — it never deletes anything from the band's actual library, only your phone's offline copies.