What is the take-home message in The Last Lecture by Randy Pausch?

The "take home message" of The Last Lecture is that our dreams must play an active role in the lives we lead.
Pausch is confronted with a challenging reality as he decides to deliver his "last lecture."  He knows that he has only months to live.  He also knows that the summation he gives should not be about dying as much as how to live life even in the face of a defined end.  This understanding determines his message:

Whatever my accomplishments, all of the things I loved were rooted in the dreams and goals I had as a child…and in the ways I had managed to fulfill almost all of them. My uniqueness, I realized, came in the specifics of all the dreams—from incredibly meaningful to decidedly quirky—that defined my forty-six years of life. Sitting there, I knew that despite the cancer, I truly believed I was a lucky man because I had lived out these dreams.

Randy's "take home message" is that individuals should live their lives in accordance to their dreams.  He believes that a dream worth dreaming drives a life worth living.  
Randy employs several key moments to communicate this message. One such moment is when he recalls painting the walls of his room.  When he paints the quadratic formula and the elevator, it is clear that Randy's aspiration will fuel his hard work. His dream of utilizing math at an early age as well as the dream of smashing boundaries through the image of the elevator helped to fuel Randy's purpose in life.
Another detail that reveals the importance of dreams in Randy's life is when he was able to meet "Captain Kirk." Randy talks about how he "imagined a world where I actually got to be Captain Kirk."  It fuels his desire to build his landscape of virtual reality and share it with William Shatner, the actor who played Kirk on the television series.  Randy's dream fueled his work as an engineer. Randy's dream also played a role in how he faces death. This is seen when he received an autographed photo of Shatner playing Kirk with the line "I don't believe in the no-win scenario."  Randy's dream and "infatuation" with Star Trek kept him "in good stead" because it fueled his life's work and assisted him with how he would confront cancer.
Finally, Randy's dream of "making it" to the National Football League (NFL) was another instance where one's aspirations provides the blueprint for how to live life. Randy wanted to be a football player, a dream that never came true.  However, in this key detail, Randy's message is that there are instances where we can derive much from not accomplishing our dreams.  When Coach Graham treats Randy in a rough manner, he realizes that Coach won't "give up" on him.  Coach Graham taught Randy the value of hard work and that our work ethic must match our dreams.  He gave Randy "a feedback loop for life." Randy's experience with Coach Graham taught him the "head fake," where we learn a life lesson "well into the process" of doing something.  This provides the inspiration for Randy's last lecture.  It becomes a head fake for his kids, an instruction manual on what to do and how to live even when their father is absent.