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Yes, you're close. To work on files with names ending in .vtk in the current directory and its subdirectories, try:
find . -name '*.vtk' |
while read file
do
printf "Do whatever you want...

Great! You are in for learning the most interesting thing there is the world: shell programming in the Unix environment!

(Well, now that i jog my memory really hard, i have to admit there are a...

This solution is based on some assumptions (using parameter substitution):
#!/bin/bash

for file in *.vtk
do
x="${file%%_*}"
x="${x//[a-z]}"

y="${file#*_}"
...

Assuming that you're using a POSIX conforming shell (such as ksh or bash), the following seems to do what you want:
#!/bin/ksh
for file in x*_y*_z*.vtk
do
printf "%s\n" "$file" | (
...