Read the play to get a feel for how the production should look. You'll be looking for clues in the script, which will tell you not only about the setting of the musical but also about the props that will decorate the set and that the actors will use during production.
Do theatrical research for the show. For example, it may be a period show, which means you'll need to know what kinds of furniture, light fixtures and properties would realistically adorn the set. Additionally, it's a good idea to do some specific research about designing for musicals. You'll want to know if past designers have encountered special problems in the design because the show was a musical instead of a straight play.
Make a list of the elements within the play---both in terms of the set and props. You'll use this as a cross reference to ensure everything is acquired during the course of rehearsals.
Design the set based upon your readings of the play, conversations with the director and the constraints of the budget. Musicals usually have very big sets and multiple platforms, like the sets used in the productions of "Phantom of the Opera" or "Les Miserables."
Buy the materials and build sets. Often the props for a musical have a fantastical element to them ---think "Phantom of the Opera"---that require hydraulic lifts. If the pieces cannot be purchased, you may have to design and build them yourself.
Acquire and design props. For example, if it's a period piece, you'll want to make sure that the furniture matches the style of the era.
Take production photos during the rehearsal process. These will be developed, enlarged and used later for decorating the front lobby and for promotional materials.
Coordinate with the publicity department to design the lobby display. You'll want to acquire a felt-covered bulletin board or a classed in photo display case. You'll put actors' photos and bios there as well as the photos you've taken during the rehearsal process. Additionally, the lobby can be decorated to reflect the play's setting as well, including copies of the sheet music for the production. These can be autographed by the actors, the director, musical director and composer and placed under glass.