How do I print at the Science Center? 
See the
Printing guide of HASCS . Note that you need to have a
printing budget . 
I tried to print my notebook but there is no
printout. 
You might have no printing budget. The printer would spit out a page telling this.
You might have written the notebook to a PS file on your computer instead of sending it
to the printer (you can chose so at the printing dialog box).

I want to save paper. How do I print out only a
part of the notebook. 
Chose "print selection" instead of "print". The selected cells will be printed.
Alternatively, open a new notebook, cut and paste the part you need to turn in into
the new notebook and print that out.

I have problem running Mathematica
on a G4 Macintosh in the Basement of the Science Center. At the
first evaluation, the program asks me for a "Math Link program to Launch".

Since Mathematica is running on a server, the Mathematica program can have problems
with finding the Math kernel (which is a seperate program).
In the window asking for the Math Link program, choose
"General Software/Math & Statistics/Mathematica 4.0/Executables/Power Mac/Math Kernel".
It will then take some time until the Kernel is fetched from the server and the first
evaluation can be done. But afterwords, things should get smooth.
