Could someone show me a simple exercise solving a curl, div and/or gradient?

I'm a college student and will be sitting a math exam soon; for some reason these operators, albeit referenced all over the place, weren't covered in the seminary - or maybe I just missed it somehow. I found the definitions on wikipedia, but I'm not sure I'm doing it right. So could someone please solve a simple curl/divergence/gradient so I can have a better idea of what I'm doing? I'd be really grateful.