First, let's compute how much protein you need. The general equation is:
weight x .4 = grams of protein needed daily.
So, someone who weighs 150 pounds would need 60 grams of protein.
(150 pounds x .4 = 60 grams)
For a while, it's good to calculate how much protein you are eating throughout they day. After a while, it'll become second nature to you and you'll be able to determine it by the kinds and quantities of foods you are eating.
The book I'm reading at the moment, Vegan for Life by Jack Norris, RD and Virginia Messina, MPH, RD spells it out simply. One tip that might be good to remember is that legumes (beans, peanuts, peas, soybean products -- tofu, tempeh, soy milk, etc) are great sources of protein. The book recommends that vegans eat 3 to 4 servings of legumes per day to get the majority of their protein.
A Serving = 1/2 cup cooked beans
1/2 cup tofu or tempeh
1/4 cup peanuts
1 cup soy milk
2 T peanut butter
That's enough information to get started on protein. Here's an article that includes a chart of sources of protein. It'll help you keep track of protein for a few days or at least will tell you what foods contain good protein.
*Click this link and scroll down a bit for A Vegan Sources Protein Chart
This is just a start. I'll look for other sources and give you a list of other charts tomorrow...
Hope this was helpful...