It's even easier than editing a textfile, try 'make menuconfig' in the directory, and you'll get a menu, where you can edit each setting.
This is, how I would do it (for a 2.6.11.11 kernel):
unpack the new kernel to /usr/src/linux-2.6.11.11
rm /usr/src/linux
ln -s /usr/src/linux-2.6.11.11 /usr/src/linux
cd /usr/src/linux
copy your old config in the directory, so you can use it as a base for the new kernel: cp /boot/config /usr/src/linux/.config
make menuconfig
make && make modules_install
Now the new kernel is compiled, you'll have to copy it to your boot dir:
cp /usr/src/linux/arch/i386/boot/bzImage /boot/kernel-2.6.11.11
cp /usr/src/linux/.config /boot/config-2.6.11.11
cp /usr/src/linux/System.map /boot/System.map-2.6.11.11
Now edit your /etc/lilo.conf, add an entry like this above the existing image entry (make sure to change the root disk to the appropriate one):
image = /boot/kernel-2.6.11.11
root = /dev/sda3
label = slack-2.6.11
read-only
This way you can still boot your old kernel, in case something went wrong.
Run lilo as root, and all should be done.
Reboot and pray :P
Hope this helps, don't give up, if it doesn't work the first few times
Good luck