I'm going to assume that you're using the Sharp ROM version 3.10 or higher (go to the settings tab, select System Info, and choose the Version tab--the ROM version is at the very bottom).
To elaborate on lardman's post, yes, du will tell you how much space the directory is taking up. If you're interested in backing up ALL your application data, then use the command he gave you. If you're JUST interested in PIM data, use this:
bash-2.05$ du /home/zaurus/Applications/dtm/
It will tell you how much data you have in your contact, calendar, note, to-do, and e-mail applications (and how much room you need on the card).
The following commands will copy all of your PIM data to an SD card:
(In the Terminal application):
First, make a folder to hold the backup:
bash-2.05$ mkdir /mnt/card/dtm-backup
Next, copy the files over:
bash-2.05$ cp /home/zaurus/Applications/dtm/* /mnt/card/dtm-backup/
Alternately, just use the Backup/Restore application (in the Settings tab). It not only backs up application data, but the applications themselves, and any other files you have in your Internal Storage. I use it all the time, works great. If you have a 32MB SD card you have enough room (the Zaurus only has 32MB of storage to work with).