Copy .config from old kernel into the new kernel:
cp /usr/src/old-kernel/.config /usr/src/new-kernel
Link the symlink 'linux' to new kernel:
cd /usr/src rm linux ln -s ./new-kernel ./linux
Merge the .config into the new kernel:
cd /usr/src/linux make oldconfig
Give the new kernel a once-over with:
make menuconfig
Build the new kernel:
make && make modules_install
Copy kernel files to boot:
cp System.map /boot/new-kernel.map cp .config /boot/new-kernel.config cp arch/i386/boot/bzimage /boot/new-kernel
Modify grub or lilo as needed (no code snippet)