This is difficult because:
- If you say you're vegetarian, you may get served fish because many people don't realize it's not vegetarian
- If you say you're vegan, lots of people won't understand and will think it's vegetarian.
- If you say you only eat plants, lots of people will still serve you cheese and eggs
- It you try to just enumerate all of the things you can't eat, you may skip some culturally-relevant items, (eg crema in Mexico, paneer in India, leverpastej in Sweden, or furikake with bonito flakes in Japan)
The best thing to do is probably to just print a sheet of paper explaining veganism in the language of the country you're visiting before you go. Something like:
Hello, I am vegan. I am allergic to food from animals. I can only eat plants.
I cannot eat: meat, fish, eggs, cheese, ...
I can eat: rice, beans, vegetables, fruits, mushrooms, nuts, seeds, grains, etc
It would be a good idea to just spend a few hours googling "vegan in country X" before you do this.
After reading from other people's experiences, try to figure out what are the most common non-vegan ingredients (eg milk derivatives, fish condiments, etc) served in that country and add them to the list above before you translate it.
The Vegan Society maintains a little book called the Vegan Passport that is designed for this purpose.
I haven't owned one, but my understanding is that they translate what veganism is in every language specifically for this purpose: so you can hand it to your waitress/waiter and they'll know what you can and cannot eat.
As far as I know, they take into account culture here, so they will specifically point out commonly-used ingredients for the given country that you cannot eat.