Before I do any of this I like to
backup my
/boot partition. It may come in handy, I've wished I'd done it:
tar -cf /home/boot.backup.tar /boot
Use -cvf if you want to see what is going on.
Most people follow idoru's advice, then type:
su
make install
Note that all of the make steps except make install can be done as a regular, non-root user. Thy shall not take root's name in vain.
Now go edit your /etc/lilo.conf file.
When that's done and you've got a dead chicken to waive over your computer, reboot and during the startup process, you'll see
LILO boot:
Hit tab for options, and type in the option for your new kernel. If everything works now, rejoice. If you see a lot of kernel panics, or Nothing Happens., take notes on what did happen (and see /var/log/boot.log), and reboot with your old kernel. Go back to make menuconfig and try again. STFW to find out what happened.