Be aware that people are vegetarians for many different reasons, and resolve difficult questions in different ways. For instance, someone who simply doesn’t like meat, might try sea-food and see if they like that. Somone who’s vegetarian for religious reasons will hopefully have a helpful list of rules somewhere.
I’m assuming you’re really interested in people who are vegetarians for ethical reasons. But still, everyone does it differently. Some people’s line is ‘has a face’ which I think is a bit shallow, but I can’t really criticise. I go for ‘well, technically, anything with a reasonable nervous system, but since I don’t want to eat little slimy things anyway, it’s a bit moot’. Some people go to extremes and rule out anything which would be killed by eating it. At this point we move to IMHO.
This is discussed a lot - you should try searching the archives, and googling.