Some useful tips for flying with your pet:

Long international flights can be as hard on your dog as they are on you. If you have long layovers (more than two hours) think about checking your pet to that destination and picking it up.

Many European airports allow you to walk about with your pet on a leash - so it's a nice break for the dog to get out and walk and be with you.
Take a care kit in your carry on - bottled tap water from your home, baby wipes (good for accidents or when something 'comes up' - they are non- toxic and leave a nice smell behind), a small brush for drool mats, and a cookie or treat.

Place a shirt or some socks that have been well worn by you (i.e. odiferous) in your pet's carrier. It's a big comfort.

If you'll be staying overseas for a while, try to stick to your routine as much as possible. Keep walks on the same schedule. Find food that's as similar as possible to what your pet eats at home. Most of the pet stores and supermarkets in Germany, where I lived, had the major supermarket and premium brands.

Take advantage of the fact that many establishments allow (well-behaved) dogs inside.

Most of all, travelling with your pet can be a pleasant experience for you and your pet if you remember to PLAN AHEAD!! Don't buy your carrier or plane tickets at the last minute. Call the airlines and get SPECIFIC information about requirements AND charges. Not all airlines charge the same amount for the same size dog and costs can be high. Get the proper certifications for both your origination and destination, descriptions of which are available from the USDA/APHIS website. And certainly, gauge your travel plans on your pet's needs and personality.
Bon voyage and good luck to all you animal lovers!