I received and email tonight indicating that I had an announcement that was waiting for my approval. "Click here to approve". I think that It should have displayed the announcement in the email, so I had an idea of what I was approving?
I approved it, then went to the website to see what it was. Did I handle this incorrectly?

You did it fine. What "Click here to approve" really means is "Click here to approve annoncement if you darn well feel like approving it." Clicking that link doesn't activate the announcement and put it live on your site -- it just takes you to your Announcement area so you can read and/or activate the announcement if you want to.