Well, the best way might be to install apt. If that is not an option you might run dselect, which was the way Debian users installed packages before apt. (Read the help for dselect before using it; it is not that intuitive.)
If you are crazy (and for some reason dselect does not work) you could use a second system to determine the dependencies you need. Before I remembered dselect I typed out the following, so I will publish it anyways..
If you have Linux running on some other machine (and you have root access to that machine) then you can set up a chroot environment that mirrors the one on the palmtop. Download the "debootstrap" shell script (download the source from http://packages.debian.org/debootstrap
) and use it to build a woody installation inside some directory (which I will call "mirrordir").
Next, use the chroot command to make mirrordir the root filesystem. Use apt to install all the packages currently installed on your palmtop. Then when you
want to install some new package, go to the chroot environment and type
apt-get --simulate install foo
and you should get a listing of the other packages that need to be downloaded and installed.
I am not certain this will work very well, and it is rather ugly. But if you are not installing a whole lot to the palmtop, it could ease the dependency hell. You might look into a package called "apt-zip" as well (I tried it once, but I could not get it to be useful.)