The European Enforcement Order is a certificate which accompanies a national judgment, a court settlement or an authentic instrument, allowing it to be enforced in another Member State.
This procedure also applies to claims against someone who does not contest the claim, where a national judge has already declared that you are owed the money in question.
To apply for an enforcement order you would normally ask the court which passed judgment on the merits of your case, and you must comply with the national requirements in that Member State.
For this procedure, the claim will be considered uncontested if the defendant has agreed with your claim either in court, in a court-approved settlement or in an authentic act, or if he never objected to it, or if, having initially objected, he then failed to appear in court (tacit admission).
The procedure is based on standard forms that you must fill in. These are available in all the EU languages, along with a lot of other information, on the website of the European e-justice portal.