Another thing that helped is reading forums like this where many people admit how nervous they are. In speech class, everyone seemed to do relatively well, so I was under the impression that I was the only person in the world that gets nervous during a speech. Just knowing that other people get nervous has helped me handle it better.
You can also take your contacts out or glasses off so you cannot see people clearly, which also helps a little.
I've also noticed that my anxiety attacks usually happen before the speech, not usually during it, and they only last a few minutes. Knowing that they will not last forever has also helped me.