If you're running Debian, you can simplify this a bit by installing kernel-package (apt-get update, apt-get install kernel-package). Do what idoru says up to and including make menuconfig, and then

make-kpkg --revision=Whatever.1.0 kernel-image
(The 1.0 in the revision name appears to prevent dselect from trying to replace your kernel package.)

/vmlinuz is going to become a link to your new kernel. Edit /etc/lilo.conf accordingly.

cd /usr/src
dpkg -i kernel-image*.deb
(The reboot is to start running your new kernel.)