Sarah, being a newbie I won't try to tell you how to pot the
dendrobium. I did a search of rec.gardens.orchids (this group) for
"potting dendrobiums" and got 117 hits. I read a few and believe the
info you need is here. Firstrays.com is a great source of info. as is
AOS.com.
You won't be far off if you repot it in a plastic pot of the same size
as the terracotta one you removed it from. After you have removed all
the dead roots and dipped it in a disinfectant solution. You will need
to consult the above sources for potting medium info. as I don't do
Dens.
You came to the right place, you just got a kid , the heavy hitters
will chime in later.
Joe T
Houston