but for now I have an application desktop in c# and I can see the output of the Arduino using a simple program
So, what's the problem with this? Why do you think you need PHP?
how will be the procedure for storing the output of the arduino every once in a database if I use with the ethernet shield??
"every once in a database"? The words are correctly spelled, but the order makes no sense.
What database? Handwaving will get you exactly nowhere.