I want to set up a dual boot with RedHat and Slackware. I don't know how to accomplish this...

I already have a working RedHat installation and don't want it to be destroyed.

I have 256MB RAM. My HD is 40GB, there are 30GB unpartitioned space...
Could anyone give me some advise how to partition the rest of the disc?
When finished installing Slackware, which config file(s) do I have to edit? Will my current boot loader be overwritten?

You have two choices, either not installing any bootloader(slackware only comes with lilo i think) during slackware setup, and use grub/lilo which you installed during redhat installation to load slackware, or installing the bootloader to the bootsector of the slackware partition and have redhat lilo/grub chainloading it.
how to configure it depends on which bootloader you use for redhat, it's the only one you need to worry about.

What bootloader are you currently using? - where have you installed it to?

Slackware has lilo, Redhat uses grub.

I only know how lilo works, so that's all I can expain about booting

Lilo has 3 essential parameters:
- location where to install (most likely your root partition)
- location of the kernels.
- location of the root device, can be assigned per kernel.

I think you could even use the same kernel for both Linux OS-es. Because the 'root' parameter is different, the system will start the /bin/init program at the other root, and the boot process will continue as it's supposed to be.

I am using RedHat and Slackware too:
You have to install Slackware and then goo to /boot/grub
and edit your grub.conf file.
The following is my one:

default=0
timeout=10
splashimage=(hd0,2)/boot/grub/splash.xpm.gz
title Red Hat Linux (2.4.20-18.9)
root (hd0,2)
kernel /boot/vmlinuz-2.4.20-18.9 ro root=LABEL=/ hdc=ide-scsi
initrd /boot/initrd-2.4.20-18.9.img
title DOS
rootnoverify (hd0,0)
chainloader +1
title Slackware
root (hd0,3)
kernel /boot/vmlinuz-ide-2.4.20 ro root=/dev/hda4 hdc=ide-scsi

I think it's intuitive. I have XP on hda1 Swap on hda2 RedHat on hda3 and Slackware on hda4.

harp's idea will work fine (although i like to keep my swap partition as the last thing on my harddrive)

basically, since u have 30 gig unpartitioned, u must have used 10 gigs and used the default redhat partitioning (the primary 100 meg /boot, the /, and the 512 meg swap)

all u have to do now is download slackware, pop in the cd, and at one of the boot prompts type cfdisk (the instructions will tell u when) and create an ext3 partition at the end of your harddrive (the program is not hard, just not pretty)

then go through the normal install, but when asked to space out partitions, tell the installer to use /dev/hda1 mounted as /boot (that way all kernels will be placed in the same place for both redhat and slack and avoid confusion later for grub/lilo)

go through everything, and i would strongly recommend that you use lilo (only because i like it and u can have cool vga modes in it)
u can add your redhat partition and configure lilo later to load the correct kernel
if not, just choose not to install lilo and use the same grub format as harp to boot slack