newbie question about DNA and cells

[Eric Hanson]

Hello,

I'm a computer scientist interested in genetics and cellular biology. 
I have a decent understanding of the process of DNA getting converted
to RNA, from there to enzymes, but have a question.

Each cell has the same DNA as its base, and yet one cell might become
a piece of tooth enamel and one might become a piece of toenail.  If
they each have the same DNA, how does the cell know what to become?

Thanks,
Eric