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)