If I have a directory /directory1 and want to tar and zip everything in it into a file new_tar.tar.gz on disk (not tape)

How can I do it?

I tried tar -cv /new_tar.tar /directory1/*

But I got an error: tar: /dev/rmt/0: No such device or address

I would personally never tar anything up with an 'absolute' file name as you'll never know whether you'll have permission to untar it/whether you'll overwrite someone's much needed directory.

I would do the following from directory1:
tar cvf home_directory/new_tar.tar *

Thank you, that tars them up perfectly.

To zip them, should I wait until after they're all tar'red, and then zip, or is there a way to zip as they are tar'ing?

Yes, you can:

tar cf - * | zip_program > tarballname.tar.gz

This is generic, so fill in where appropriate. Some compression programs need a flag to go to standard out so double check.

tar by the name is "tape archive" so it assumes, if "-f" option wasn't provided it tries to put file on the tape drive: /dev/rmt is a acronym of tape drive in UNIX.

So you give it "-f" option and a file name to redirect archive to file and not to tape.

Today's tar is quite improved so there's no need to use compression as a separate program. Just add "z", like "tar -cvzf". Some versions of tars take the list of parameters without "-" but normally it is required. Get "UNIX Essentials and UNIX Core" DVD or "UNIX in 24 hours" as they teach all this stuff.

Hope it helps.