thanks a lot!
I'm a native Russian-speaker. I don't know Ukrainian in a sense that I never learned it.
But I actually like reading, Russian classic literature included, so I know a lot of Slavic and Russian archaisms. Plus I grew up in Russian/Soviet cultural environment so I picked up a few Ukrainian words from the media. Also I drove through Ukraine a couple of times.
As a result when I watched streams of the "Euromaidan" from Ukrainian TV channels (Громадьске-ТВ, if I remember right) I could understand 90% without using a dictionary or any other reference. Although as I was told the western dialects are harder to understand due to a great Polish influence, can't say anything about it.
I can't give you examples, because as I said I don't know Ukrainian, I can't formulate my thoughts in it, but I can understand it.
why would not you go to online dictionary and check? For native speakers they are not very different, for you -- different enough to be independent language which requires a lot of efforts to learn (count existence of dialects, when Ukrainian speakers from the East and West do not understand each other 100%).
If you were fluent Russian speaker, who can read classic literature and folklore tales without dictionary - we could say that it is not that far from Russian.
Simple answer, no, Ukrainian and Russian languages are not very different.
Ukrainian language is much older than Russian, generally is based on old Slavic language, while Russian is based on other languages. Remember Kievan Rus came first, Russia as term came much later.
Even today there are disputes - is ukrainian language or dialect of russian. If it would too different languages, there wouldn't such disputes.