How to use nonce in front end post submission form

Thanks to a variety of posts around the web I’ve managed to put together a front end submission form. After about 24 hours of tweaking I’ve finally got everything working including a redirect to a ‘success’ page after submission, but I have no idea what to do with the nonce.

Here is the form page: http://pastebin.com/YWyXL3jY

And here is the success page: http://pastebin.com/3Usu0Pt6

They are both custom page templates (I know the formatting is a bit all over the place at the moment as different parts came from different sources, and I don’t think I’m going to use the file upload feature as I’d rather use a plugin for better security).

Does the nonce need to be processed before the user is redirected to the success page? I have no experience at all with nonce’s and am kind of a ‘copy and paste’ coder when it comes to PHP so please be gentle!

Huge thanks for any advice anyone can give 🙂