for slackware I go to kernel.org and download the newest 2.6 kernel to /usr/src then
Code:
cd /usr/src
tar xvfj newkernel.tar.bz2
rm linux
ln -s newkernel linux
cd /usr/src/linux
make menuconfig
make modules_install
make install
this will put your new kernel in /boot as vmlinuz
if you have another vmlinuz there it will become vmlinuz.old
add a new entry with vmlinuz.old to save the old kernel
for lilo run lilo
for grub edit /boot/grub/grub.conf or /boot/grub/menu.lst