Reading Walter Kaufmann´s "EXISTENTIALISM. From Dostoevsky to Sartre", with selected readings. It is an inspiring as well as sobering account, and seems to serve well as an introduction.
"The existentialist has tried to bring philosophy down to earth again like Socrates", Kaufmann wrote (in 1956), "but the existentialist and the analytical philosopher are each only half a Socrates. ... (I)f the feat of Socrates is really to be repeated and philosophy is to have a future outside the academics, there will have to be philosophers who think in the tension between analysis and existentialism."