Russian Cases

[sunniegreen.livejournal.com]

Hi, I'm an American student learning Russian. The vocabulary, I am slowly accumulating, the pronunciation needs some practice but isn't any real trouble. The things I was scared of aren't so scary. My problem (and the problem of the rest of my class) is with the cases. Our professor, bless her heart, is having trouble explaining them to us clearly. Personally I think that it can be harder in the lower levels to be taught by a native speaker because there is not as much mutual understanding of the problem areas.
We've asked for clarification and parsing sentences but she doesn't seem to have much attention span for explanations because she doesn't seem to understand what we aren't understanding. It always seems to be one step forward, one step back, one step forward, and suddenly you're in China and you're holding a wedge of cheese and you don't know what happened but nothing makes sense anymore.
Anyway this is my long winded way of asking, does anyone have a good general case-usage explanation? Maybe a few sentences showing where cases are in use? I've seen single sentences and phrases, but it is hard to understand the whens and whys without seeing them in action. Maybe a chunk of text with cases pointed out? For anything, I would be eternally grateful. Thanks!

(no subject)

[upthera44.livejournal.com]

There is a character in Joseph Conrad's novel "Under Western Eyes" (which is about Russian revolutionaries) named Nikita "Nekatur". Can someone tell me what the word "nekatur" might signify in Russian? It's something negative I assume, but beyond that don't know.