Hi,
The only directories you must have in the root partition are as follows :
/
/bin
/dev
/etc
/lib
/sbin
So, depending on your existing partitioning arrangements you can move things like /var, /usr, /home to physically separate partitions, preferably on other disks. If you have the hardware, you can back up your root partition to tape, plug in a new drive with suitably sized partitions and restore from tape onto the new drive. Then swap the new drive for the old one (you might need a boot floppy to cover the lilo side - i.e. boot from floppy then install the boot loader in mbr or partition as appropriate).
As a first action you might like to look in /var/log and its subdirectories to see if there are any unwanted log files you can dump to free up space.
Regards