In a word: You need to plan ahead.
Of course, the scary thing is that even if you plan ahead, things might not go according to plan. I've read multiple stories about people who were unable to travel because the airline did an about-face and informed them at the time of their flight that it wasn't safe and accommodations would not be made.
Luckily for us (knock on wood), my son doesn't have any airborne food allergies, so the flights aren't my biggest concern. I'm more concerned with finding safe foods for him to eat at our destination, so I've started doing some research to prepare for our trip. If you're in the same boat, here are a few things I've learned (and if you have any tips to share, please let me know!):
Start at FARE, an organization whose "mission is to improve the quality of life and the health of individuals with food allergies, and to provide them hope through the promise of new treatments." They have an entire section dedicated to the topic of traveling with food allergies. I've already downloaded their Food Allergy Chef Cards, which you can print out in multiple languages and show at restaurants to explain your food allergy.
Then search for tips about traveling to your specific destination. Find out what the food labeling laws are, and how accommodating society as a whole is. You can also find tips on identifying safe places to eat, such as enlisting the assistance of the hotel concierge for possible locations nearby, or seeking out halal restaurants, because they usually know exactly what ingredients are in their food.
Of course, you should also carry epinephrine and any other medications at all times. In fact, I'll be ordering a refill so we can take extra epi-pens with us when we travel.
If you've traveled abroad with food allergies, how did you make sure the food was safe for you?