After a campaign has been sent, basic numerical statistics will be returned in the XML when you request campaign details. If you are using one of our wrapper libraries, there are functions in those libraries to make such calls.
If you're working with your own code, the documentation for requesting campaign details will give you a start, but if you want to drill down for more details, you'll need to make calls for campaign events, as documented here.
I hope this gets you started down the right plath. Let us know if you have additional questions.