Two main steps needed:

1. Create /etc/init.d/dropbox

Change DROPBOX_USERS to include all users that want to run dropboxd (separated by spaces), and save the file to /etc/init.d/dropbox. You need root permission to do it. You might also have to specify the full path to start-stop-daemon if it is not in your $PATH

#!/bin/sh
#dropbox service
DROPBOX_USERS="user1 user2"

DAEMON=.dropbox-dist/dropbox

start() {
   echo "Starting dropbox..."
   for dbuser in $DROPBOX_USERS; do
       HOMEDIR=`getent passwd $dbuser | cut -d: -f6`
       if [ -x $HOMEDIR/$DAEMON ]; then
           HOME="$HOMEDIR" start-stop-daemon -b -o -c $dbuser -S -u $dbuser -x $HOMEDIR/$DAEMON
       fi
   done
}

stop() {
   echo "Stopping dropbox..."
   for dbuser in $DROPBOX_USERS; do
       HOMEDIR=`getent passwd $dbuser | cut -d: -f6`
       if [ -x $HOMEDIR/$DAEMON ]; then
           start-stop-daemon -o -c $dbuser -K -u $dbuser -x $HOMEDIR/$DAEMON
       fi
   done
}

status() {
   for dbuser in $DROPBOX_USERS; do
       dbpid=`pgrep -u $dbuser dropbox`
       if [ -z $dbpid ] ; then
           echo "dropboxd for USER $dbuser: not running."
       else
           echo "dropboxd for USER $dbuser: running (pid $dbpid)"
       fi
   done
}

case "$1" in

   start)
       start
       ;;
   stop)
       stop
       ;;
   restart|reload|force-reload)
       stop
       start
       ;;
   status)
       status
       ;;
   *)
       echo "Usage: /etc/init.d/dropbox {start|stop|reload|force-reload|restart|status}"
       exit 1

esac

exit 0

2. Make the script executable and add it to the system startup

sudo chmod +x /etc/init.d/dropbox 
sudo update-rc.d dropbox defaults 

3. For Debian you might need to add to the very beginning:

### BEGIN INIT INFO

# Provides: dropbox

# Required-Start: $local_fs $remote_fs $network $syslog $named

# Required-Stop: $local_fs $remote_fs $network $syslog $named

# Default-Start: 2 3 4 5

# Default-Stop: 0 1 6

# X-Interactive: false

# Short-Description: dropbox service

### END INIT INFO