Yisela makes a good point about the use of modal dialogs. Confirmations are a perfect case for contextual presentation. However, that's not always the best experience or even possible.
One other alternative to consider before settling on a new page is to load the confirmation into a relevant position on page asynchronously (ie, ajax). Content rendered directly into the page is, in many cases, more user friendly than modals.
If all else fails, sometimes a new page with very little content is the best or only way to go. Your primary concern is to make the confirming message clear, concise, and unmistakeable. Then give the user an easy way to move on to their next most likely task(s).
Your layout should use simple, spacious typography; icons or images as necessary to reinforce the action; color fields to focus attention (depending on the UI guidelines); and well organized white space to pull the user directly to the message.
As for where exactly, that's up to your page templates and the flow of your site.