iOS 7 supports your device. Plug into the wall and not the computer. Just apply the update via letting it do it on its own. it takes around 1.5 hours to completely download. When you see the Welcome screen follow the screen prompts.
Have your Apple ID handy, you will need that and your Apple Password. After its completed all should work ok.
However please be aware some people have had install issues which are addressed at the http://www.apple.com help forums.
Oh gee, I was told to plug it into a computer, and that didn't work, so I will try later to plug it into the wall. thank you so much!I will let you know if it works.
plugging into the computer via itunes is another way to update. I have read its buggy doing that way. update via over the air with the phone plugged into the power outlet. much easier.