You have two options:
1. Save into the 16MB FlashROM area where your operating system - also called ROM - is located. Your operating system does not take up all the space and there are about 2MB left.
2. Save to a CompactFlash, SecureDigital or MMC memory card.
Option 1 is _not_ possible with the standard Sharp ROM (that comes in a brand new Zaurus). You have to replace your ROM with another one which allows writing to the FlashROM area. Replacing a ROM is detailed in several HowTos both here at ZUG and at OE.org.
For Option 2, you obviously need a memory card. These days they are very inexpensive and they make your Zaurus much more useful. For example, I have a 512MB CompactFlash card where I carry about 8 hours of music to listen to. Buying a memory card is a very good idea.
In any case, you will need to tell the system to save the file to a non-RAM location. In most applications, this can be done when you are saving a document. Otherwise, you can go to the Documents tab, press one of the document icons and _hold_ the stylus down until a Properties window shows up. There you can change the location of the file - you will get a menu listing all available locations.