__ Get your papers in order. Passports/visas for the whole clan should be applied for 10 to 12 weeks before takeoff. Everyone traveling needs travel documents -- even newborns. It takes time for applications to be processed, so don't leave it until the last minute. If you have a passport, check to make sure it hasn't expired -- and won't expire before the return date of your trip.
Some countries also require passports to be valid six months or longer beyond the dates of your trip, so check entry requirements before you go (see link below). Passports can be rushed for an extra charge, plus overnight shipping costs. If your trip is less than two weeks away, contact your regional passport agency (travel.state.gov/passport/about/agencies/agencies_913.html) and be very polite to expedite the process further. If only one parent is traveling, you'll need one more piece of paper: a letter, preferably notarized, stating that the non-traveling parent gives his permission for the child to leave the country.
Find out the type of identification you need for your destination(s) by checking the U.S. Department of State's foreign entry requirements page: travel.state.gov/travel/tips/brochures/brochures_1229.html
For passport/visa information and applications:
__Make sure your child's car seat is approved for airplane use. Look for a sticker stating that the seat is plane-appropriate. For a proper fit, the car seat should be no wider than 16 inches. If your child weighs less than 20 pounds, the AAP recommends using a rear-facing seat. If your child weighs between 20 and 40 pounds, the seat should face forward. Children over 40 pounds can use regular seat belts safely.
__ Purchase tickets for an evening flight. This shouldn't be hard since most flights to Europe are overnight anyway. Flying at night may help avoid disrupting your child's -- and your -- sleep schedule. Also, if they're snoozing, you don't have to entertain them! It might be harder to find an overnight flight home, so be sure to have lots of snacks and distractions on hand for the return trip.