You will want to download the Dutch language pack for both Store & EE. Then in the Super Admin account you will want to set Dutch as the language that EE uses and make sure that members prefs control the site. From there Store should use Dutch in the CP and for error messages.
Another thing to mention that if you are using inline_error handling you can create custom error messages in your template instead of using the default store messages.
For example lets say you have a form that has
This would show the default Store error message if the user did not fill it out. If you change it to something along the lines of
Whoa buddy! We can't sell you something without knowing your name.
You can change the message that is shown to the user.