It's said we only have a handful of the plays of Sophocles, Euripides, Aeschylus, etc. How did the plays we do have actually survive? And how do we know there are so many missing?

I suppose my question is really in two parts:

1. How does a ~2500 year old play survive such that we can be reasonably certain of its authenticity and authorship?

2. How can we have evidence of, but not the text of, lots of other such plays?