To build:

git clone git://busybox.net/busybox.git
cd busybox
# read INSTALL
make menuconfig
# install ad lib

I prefer to install it to a separate directory like /busybox

To use busybox init, I use it all the time:
add init=/busybox/init to the kernel command line
create an /etc/inittab, mine looks like:
::sysinit:/etc/rcS

tty1:12345:respawn:/sbin/agetty --noclear 38400 tty1 linux
tty2:12345:respawn:/sbin/agetty --noclear 38400 tty2 linux
tty3:2345:respawn:/sbin/agetty --noclear 38400 tty3 linux
tty4:2345:respawn:/sbin/agetty --noclear 38400 tty4 linux
tty5:2345:respawn:/sbin/agetty --noclear 38400 tty5 linux
tty6:2345:respawn:/sbin/agetty --noclear 38400 tty6 linux

::ctrlaltdel:/root/bin/Off

create an /etc/rcS that starts up whatever you want or just
look into your look into the files below /etc/init.d/ and
extract whatever what thoose actually does.

Since shutdown doesn't work with busubox, you have to decide how
to take down the mashine, a simple busybox poweroff could work.

I cannot give a remote presentation since I dont have enougth bandwidth
and no suitable camera+microphone, otherwise I wouln't mind.

Note, if you are using an initrd/initramfs you are already using
busybox.

Regards,
/Karl Hammar