Having worked internationally in Berlin and Amsterdam, many people ask ‘how did you do it’? First, have the gumption. Trust when you jump out into the universe, it will catch you and you'll land safely. It helps to have a good portfolio, a nest egg, and a lot of luck.
With friends, I took a backpacking trip through Europe, made it to the Love Parade in Berlin, visited castles in Spain, and interviewed at agencies along the way.
You'll want to do your research upfront on good shops. Arrange a good time to visit, (when everyone is not ‘on holiday') and loosely schedule interviews ahead of your trip. Hopefully, you'll have a good headhunter or recruiter to represent you. If you can't get a real interview, ask for an informational interview to get your foot in the door, or request feedback on your portfolio.
Let's say a Creative Director is looking for a new team, and you come across his or her radar at the right time, the stars are aligned, and you get hired. Larger international agencies should have the resources to hire an international lawyer for your living and working visas. Finding a place to live can be daunting if you don't speak the local language, but there are services (for a fee) to help you out.
Once you land at a shop, preferably somewhere good, you'll have a whole new world ahead of you. My experience has been that most ad agencies work the same way in Europe, as they do in the states. However, it will take some time to figure out the local customs, how to get around, and the language. (Don't be a 'stupid American' who refuses to learn the local language. Yes, English is the international business language, but you need to make an effort.)
By the time you're settled in, you'll be off on an amazing adventure that will change the course of your life's DNA forever!