Depending on where you're traveling, it's not hard at all. The tricky part is when you don't speak the language and can't fully understand the menu.
For the most part, however there are tons of options. Don't forget, nobody eats 100% meat all the time. You may need to be fairly open minded (again, depending on where you are going), but you definitely won't starve. There will always be meatless side dishes or appetizers you can have as a meal, if no vegetarian main course is available.
If you're vegan on the other hand, you'll need to be extra careful as you never know when animal fats, eggs, honey, etc are added to restaurant food... especially if you can't read the menu.