My previous conversation with an employee at a Caribbean restaurant, it took less than two minutes:
Employee - 'Hello, your through to the Turtle Bay Restaurant'
Me - 'Hey, I was wondering what on your menu is vegan?'
Employee - ' Hi there, give me a second I will pull up our list....'
They then read out their options.
Another option is to use an eating out guide, there are several out there, and two of them are,
Happycow
www.happycow.net