A good internet place to begin is :
Here are some introductory books to consider:
Walter Kaufmann, Existentialism from Dostoyevsky to Sartre
Paul S. MacDonald, The Existentialist Reader
Both contain selected texts and introductions/commentaries.
William Barrett, Irrational Man:A Study in Existential Philosophy
Beginning with Nietzsche and Kierkegaard, the existentialist movement includes many of the most important Continental philosophers since 1900; it is important to remember that Existentialism is not a school of thought but a label that includes many different perspectives. One cannot read just a few texts and say to oneself, "Ah! so THAT is what it's all about."