Most vegetarian restaurants in Taiwan, especially pay-by-weight buffets, noodle stands and most other small eateries use the characters 素食 (su4 shi1) in their name, and many more have a large sign with just these characters to advertise a vegetarian restaurant to passers-by. It's well worth learning to spot these characters, ideally before coming to Taiwan.
As convenient as this is for vegetarians in Taiwan, it is slowly changing, with an increasing number of vegetarian restaurants now using 蔬食 (蔬 = 'shu1' = vegetable) in their name instead, but these are still the characters to look out for when hungry.
For a 'lesson' on Chinese characters, see this post.
From my experience, few vegan restaurants use these characters, so usual fake meat warnings apply at these restaurants, but most still have plenty of vegetable-based dishes, and rice and soup.
This is a kind of a 'Where's su shi?' version of the classic 'Where's Wally?'. A link to the answers is at the bottom of the page.
These are all old photos, mostly from a scooter trip around Formosa in 2009. I do not know where the individual photos were taken.