For the mathematical answer to your question, go here:

Probability of a Random Variable in the Normal Distribution
Press the appropriate probability button, in this case, the third one, and Enter 0 and .667 and press the Calculate button. It will show you the math.

Now, for an in depth description. The normal distribution follows a bell curve, the theory being, that 1/2 of all possible cases rests at 0, based on a Z score which is (X - mu)/sigma.

With respect to your table, everybody works differently. I have a book that uses 2 decimal places. For you, I'd round and look for 0.67. If you want to split hairs, you can interpolate between 0.66 and 0.67 if you are familiar with interpolation.

Or, use Excel for exact decimals: =NORMSDIST(0.667)-NORMSDIST(0)