This question mostly refers to the kind of business you carry out and with whom you carry it out. Check if specific legislation exists for your situation or your type of business. While EU Data Protection Directive 95/46/EC has harmonized the substantial part of data protection law in the EU and the European Economic Area, enforcement of the rules is still up to national authorities and courts.
This means that in most cases national courts will be the ones who decide on the basis of European Law. In a country the national law (for example civil procedure law) regulates which court works on a procedure. The same applies if the help or counsel of a data protection authority is being sought.
The General Data Protection Regulation will further simplify how national data protection authorities coordinate investigations among them which should result in more legal clarity. The relevant provisions can be found in Articles 55-62.
Furthermore, the European Union has setup an online mechanism which allows businesses and consumers to settle disputes without courts. The site is available in all official languages of the EU and can be found via https://webgate.ec.europa.eu/odr/. This “online dispute resolution” mechanism cannot only be used for consumers to make a complaint against a trader, in some countries it is also possible for traders to submit a complaint against a consumer.
Everything can be done online in four basic steps: 1. Submit a complaint, 2. Agreeing on a dispute resolution body, 3. Complaint handling by the dispute resolution body, 4. Outcome and closure of complaint.