Can you explain Russian grammar to me?

Well, the biggest difference between Russian and English (and the same thing that makes it more difficult) are the declensions that Russian possesses.

Russian nouns have three genders: masculine, feminine and neutral. Adjectives must agree with nouns, the number and the gender plus all have to be in the right declension.

For example:

красивая женщина - с красивой женщиной

красивые женщины - с красивыми женщинами

(krasivaya zhenshchina - s krasivoi zhenshchinoi

krasivyje zhenshchiny - s krasivymi zhenshchinami)

a beautiful woman - with a beautiful woman

beautiful women - with beautiful women

Note the ending. It keeps changing always and that's the most difficult part of Russian, although these things are pretty regular.

The other tough thing is the verb conjugation but Russian doesn't have as many tenses as English, so it's pretty much a relief too.

Russian also has a huge vocabulary and loads of suffixes. It's a pretty rich Slavic language. You should do a lot of reading in order to remember all the words.

You can also read the wikipedia on Russian Grammar, it will give you a picture: http://en.wikipedia.org/wiki/Russian_grammar