On http://www.harald-schreiber.de/ there's a complete HOW-TO in English for all the Casio Exilims, even if you use an older kernel.
Here's a very short and easy HOW-TO: Acces the storage of the camera, that works if your Kernel has USB-Support:
1) Make a Dir for the camera. For example /media/camera or /mnt/camera
> $ mkdir -p /media/camera
2) Then choose one of the following lines that matches with your system and append it to the file /etc/fstab
a) If you have no SCSI disks: /dev/sda1 /media/camera vfat ro,noauto,user 0 0
b) If you have one SCSI disk: /dev/sdb1 /media/camera vfat ro,noauto,user 0 0
c) If you have two SCSI disks: /dev/sdb2 /media/camera vfat ro,noauto,user 0 0
and so on....
REMEMBER that you have to change the camera-dir of this line if you don't use /media/camera
ALSO REMEMBER that you have to activate the USB Button on your Exilim USB Cradle Base, otherwise it won't work!
IN SOME DISTROS you have to run
-mount /media/camera but in Mandrake 9.2 it isn't needed.
This should also work with other Exilim models, not only with the Z3, but please search in google or harald-schreiber.de for more information.
I haven't tried the software that is included in the Exilim Pack but I think the Photo Loader needs the Internet Explorer, so it will only work if you have the Internet Explorer running on Wine.
I only tried the Kodak Easy Share software but it didn't work with Wine and even with CrossOver Office I couldn't get it run. But GIMP has much more Options, so don't worry.
It could be that something in this review is wrong because I'm still a Linux-Newbiee, but you will find more solutions if you search in google.

What "fedivh" writes sort of works for me (Mandrake 10.0 Official), except I can only read the images -- movie clips just don't show up, which is a major point.