You apply with your CV (and cover letter, etc.) and also complete interviews if you are fortunate enough to be selected. There is no large-scale application process for the country, you look and see which hospitals and clinics are hiring in areas that interest you, and you apply directly to them. If they like your credentials, then you get an interview. If they like you in the interview then you might get hired.
You can apply on your own, or through an agency, it is up to you... but you want a GOOD agency, that gets paid by the hospitals and does not charge the doctor anything.
Your grades are BY FAR the most important thing, along with language skills. Yeah, research looks good, and other experiences might help you get a foot in the door, but if you have crap grades and cannot speak German fluently, then you are not going to be likely to get an interview no matter how much research you have done or how many clubs you have joined. In addition, the color of your passport plays a huge roll in getting hired in many EU countries. Do not overlook that. There are some places where a non-EU citizen has a shot, and others where you can totally forget about it. Laws are not uniform throughout the EU in that regard.
"When I haven't any blue... I use red."
- Pablo Picasso
BA - Oregon ° MS - BYU ° MD - MU-Sofia
Urology Resident; Clinical Research Fellow