Please see the Overview for the general introduction to this series.
Thai food can be heaven for a vegetarian as long as you know a couple things to watch out for. Almost any dish can be made with Tofu instead of chicken, beef or shrimp. The biggest problems are fish sauce and shrimp paste. Also, as with most cuisines, soups are made from meat-based stocks.
The fish sauce issue is fairly easy to deal with because it is typically added at the last minute, so as long as you can communicate with the waitstaff you can ask for it to be left out. The Thai name for the sauce is "Nam Pla".
Shrimp paste is harder because it is often in the prepared paste for most of the curries (red, yellow, green, massaman, panang, etc). You will have to ask a lot of questions to feel confident that you can get a curry without it. So as a fallback position if you feel that all you can communicate is "no fish sauce", your best bet is probably noodle dishes such as Pad Khee Mao (drunken noodles), the well known Pad Thai, or fried-rice style dishes.
Occasionally you will find a Thai restaurant that specifically caters to vegetarians, such as the wonderful Tawon Thai in Seattle’s Fremont neighborhood. Any dish that can be made completely vegetarian is labeled on their menu with a "J" (for Jain)! If you make it there, I highly recommend the Kao Soi. OMG is that good, but don’t wear your nicest white shirt!