In Speak, what was Melinda's journey, and why did she embark on it?

Melinda's journey in Speak is to find a voice taken away as a result of being sexually abused at a party the summer before her first year of high school.

The sexual assault Melinda suffers at the hands of Andy Evans takes her voice away.  The trauma she experienced in addition to everyone in her social group blaming her for calling the police and breaking up the party where the rape took place contributes to her silence. As high school begins, Melinda finds herself socially ostracized.  She is unable to fit in anywhere and with anyone.  As a result of social and psychological marginalization, Melinda is unable to "speak" in a literal and symbolic way.

Reclaiming her voice constitutes her journey.  She has to navigate many different obstacles in her path such as uncaring teachers, even more unfeeling students, and, of course, "IT."  She must voyage through the painful condition of nothingness in order to find her voice: "I wash my face in the sink until there is nothing left of it, no eyes, no nose, no mouth!  A slick nothing!" Melinda finds some sources of assistance on her journey, such as the sage-like words of her art teacher:  

When people don't express themselves, they die one piece at a time.  You'd be shocked at how many adults are really dead inside- walking through their days with no idea who they are, just waiting for a heart attack or cancer or a Mack truck to come along and finish the job."  It's the saddest thing I know.

Melinda's journey takes her through intellectual stopping points, such as comparing herself to Hawthorne's heroine, Hester, in The Scarlet Letter: "...S for silent, for stupid, for scared.  S for silly.  For shame."  Her quest requires her to recognize the obstacles in the outside world and rise above it: "It is easier not to say anything... Nobody really wants to hear what you have to say." 

As her first year of high school comes to a close, Melinda is able to find her voice.  She emerges to this point as "tears dissolve the last block of ice" which blocks her ability to speak.  She is able to experience the "dripping shards of ice that vanish in a puddle of sunlight on the stained floor. Words float up."  Her confrontation with "IT" one last time is when Melinda comes full circle in her journey.