Please read the "Writing a proposal" chapter from the GSoC student guide. The full guide is a must read if you want to apply.
Some more specific information for MuseScore.
Please provide your full name.
Email / IRC / WWW / GitHub
Where can we contact you? If you frequent our IRC channel (#musescore on irc.freenode.net) please let us know what your nick is. If you don't, then you'd better connect and introduce yourself! If you have a web page you'd like us to know about, please include it. If you have a GitHub profile, or some other public places where you publish code, please include it.
A short description
Benefits to MuseScore
Describe how your project will benefit MuseScore. How will it benefit musicians using MuseScore to create scores? Will it be an aid for future MuseScore development?
Provide a user-level summary of the final output or results of your project. How does it integrate in MuseScore and how does it cooperate with the rest of MuseScore's features?
A more detailed description.
How long will the project take? When can you begin work?
Include an estimated timeline of the project with mini-milestones
Please also note any vacation time you expect to take during the project period.
Who are you, what are you studying (and where), and what activities do you enjoy? What is your experience using MuseScore or other music notation software? What (music) code development projects you've realized? What makes you the best person to work on this project? Are you a musician? Which instrument(s)? Google Summer of Code is about code. Did you participate to other open source project? Wrote something on your own?