Have I graduated from a master's course?

What is the correct phrasing to tell the people that I have successfully obtained a master's degree? I want to convey the idea that I have had all classes and defended my dissertation.

BTW, is "defending the dissertation" a meaningful and correct phrase?

Having met several people who have finished their Masters, there is one phrase they use all the time:

I have finished my Masters...

EDIT: In view of the OP's comment below, there's also the variation:

I finished my Masters...(number of years ago, etc.)

The normal phasings are "finished my master's [degree]", "obtained my/a master's [degree]", or "have my/a master's [degree]". The word degree is optional in all phrasings and should be used where it sounds better. It is frequently omitted when naming the subject (i.e. I hear "master's in engineering" more often than "master's degree in engineering"), but including it still sounds completely normal.

As for "defending the dissertation", that is both meaningful and correct, but it is not terribly common to use the word the in that phrase rather than a pronoun. You more often see "defending his/her/my/your disertation", even when context has already established which dissertation is being discussed.

We often have authors (with PhDs and DVMs) write that they have earned their degrees.

Also, as the questioner wrote, I think it is most standard to use the apostrophe with the word master’s. See The New York Times article "The Master’s as the New Bachelor’s" http://www.nytimes.com/2011/07/24/education/edlife/edl-24masters-t.html?pagewanted=all

So your sentence could be: I earned my master's degree from State College.

First of all, congratulations on your accomplishment. As a fellow M.A., whenever anyone asks, I always phrase it as "I have a Master's Degree." This conveys everything you are looking for, I believe, and does so quite simply.

If you need a contrast, when I was in grad school, my phrasing was "I am working on a Master's Degree."

It is best to simply say:

I hold a Master's (degree) (in ...).