I am actually taking my dog to Europe next week! Each country in Europe has different requirements.
Do you know what countries you are looking at? What kind of dog? What time of year are you planning to depart?
Most countries provide the information needed on their consulate website and most EU countries require the dog to be microchipped, to have a health certificate (from a registered vet) and a Form 998 in their language (basically a vaccination form translated). England, Ireland and Sweden have very strict rules to avoid a quarantine, but it can be done.
Definitely start the process as early as you can! We are extremely fortunate to have found a vet that specializes in pet travel, so he knows the drill very well, but a vet that is new to the process may need some time and help understanding the correct procedures and when and where to send the forms off to.
In regards to flying the dog, it makes a huge difference what size he is. Smaller is definitely better for traveling.
I've done a lot of research, so I'd be glad to share everything I've found with you.