I have a graduation announcement that is a flat card, no fold. Where do I put my picture and name card?

Depending on the size of the announcement, you might be able to enclose it in another card with your pic and name card.

Just put both loose in the envelope, or tape the pic to the annoucement and leave the name card loose. There really isn't a right or wrong on this.

If you can't put it in a separate envelope as tickle suggested, I would invest in small pieces of vellum paper (that tissue paper type stuff) to put between the announcement and your name card/picture. That way, it will protect the embossing of your grad card and separate the three things.