Depends where you're going in the EU, I guess - it's not all the same at all.
Speaking for France, you need to get (1) a certificate of conformity from the French representative of the manufacturer (100 Euros); (2) Pay to register it (500 Euros).
In my case ('84 34L), No.1 proved to be impossible, since Yamaha France thought my bike was a 3AJ and put lots of "must change this" remarks on my conformity document. These were impossible to do (like I have to put a certain Yamaha part number exhaust on the bike, which doesn't fit) and thus it's been impossible to register.
Aha, I thought, there's a classic bike scheme where you don't have to conform to technical regs for vehicles over 25 years old ... so I waited a year until she passed her 25th birthday ... then they changed the rules to make it 30 years old ... so I'm still waiting :-(
French rules, gotta love 'em.