Automator Change to directory of dropped files before running Shell command

This is very easy in zsh. You can use the :h option to a variable to refer to the head of its full path:

#!/usr/bin/env zsh -f

PATH="/usr/local/bin:/usr/bin:/usr/sbin:/sbin:/bin"

for i in "$@"
do

    FILE="$i"

    cd "$FILE:h"

    # do other things here

done

In a shell like bash you would need to use the dirname command:

#!/usr/bin/env bash

PATH="/usr/local/bin:/usr/bin:/usr/sbin:/sbin:/bin"

for i in "$@"
do

    FILE="$i"

    DIR=$(dirname "$FILE")

    cd "$DIR"

    # do other things here

done