Hi people
Normally, this is the sequence I follow to compile/install a new kernel
0) make a backup of my current vmlinuz and all my /lib/modules/Žuname -rŽ folder
1) cd /usr/src/linux
2) make menuconfig
3) make
... those 3 steps build the kernel (in kernel 2.6 you don't need to do "make bzImage", in kernel 2.4 you need). Make sure to compile your root filesystem (e.g. ext2, reiserfs, xfs) in the kernel and not as a module.
4) make modules_install
5) manually copy the following files to a safe location:
/usr/src/linux/.config
/usr/src/linux/System.map
/usr/src/linux/arch/i386/boot/bzImage
...If you are compiling for a x86_64, for example, (with for example $make menuconfig ARCH=x86_64) just change the i386 with x86_64.
6) rename bzImage to vmlinuz and copy it to /boot
(I am a bit lazy. If you want you can rename it to something like vmlinuz-test; but you have to specify an entry for that kernel image in /etc/lilo.conf)
7) run lilo
8) cross your fingers and pray

May the Force be with you!
9) If something goes wrong, you can boot with the Slackware CD #1 and reinstall your kernel and modules (or reinstall a stock kernel and the stock modules).