[from BBCi's h2g2 webpage about Russian]

Alphabet
Russian has a standardized print alphabet of 33 letters, or 32 if you don't count 'yo' (ё) as a separate character. This alphabet closely resembles the Greek one, with some additions and changes of sound value. There is also a script alphabet, which is not standardized. Several letters in script can be written in two or three different ways, often by the same person. This is also Greek-based, but not so clearly. The letters of the Russian alphabet don't have names like their Greek counterparts; they are named for how they sound in a word, with the exception of two letters that have no sound of their own. These are known as hard sign and soft sign. The former is now used only for the sake of spelling the words correctly, having no real value, while the latter functions like a silent 'e', and can fall anywhere in a word. The Russian alphabet is known as Cyrillic, and is traditionally said to have been designed by Saint Cyril.

Grammar
Russian is a highly structured language. It has 6 cases (as opposed to 3 in English), which are as follows:

Nominative indicates the subject:
"John buys the newspaper."

Genitive indicates possession:
"John's newspaper is cheap."

Dative indicates the indirect object:
"John writes to the newspaper."

Accusative indicates the direct object:
"John buys the newspaper."

Instrumental has the sense of 'with' or 'by means of':
"John swats a fly with the newspaper."

Prepositional indicates location or topic of conversation and is governed by the prepositions 'in', 'on', 'about', and 'in the presence of':
"John talks about the newspaper."

Russian also has three genders of noun (masculine, feminine, and neuter). Each gender has several different types, which are declined slightly differently. The adjective must agree with the noun, so it has to be declined, too, along with the pronoun.

The verb has an imperfective and a perfective aspect, the difference being whether you are initiating an action or describing it in general ("I want to drink coffee."), or completing it ("I want to drink my entire cup of coffee."). It sounds a bit sloppy in English, but it works in Russian. The transitions from imperfective to perfective vary among the verbs; some change aspect by gaining a prefix, like the verb "to read." In this example, chitat becomes prochitat. In other verbs, such as "to go/walk," the root or suffix changes, in this example from hodit to idti. There are six conjugations for each type in the future tense. The same goes for the present imperfective - you can't have a present perfective. There are two classes, which are conjugated differently. Past and conditional tenses are arranged somewhat more simply.

Another thing to be noted about Russian verbs is that "to be" is seldom used in the present tense, and hardly ever in conversation. That is why you will often hear a native Russian speaker who is learning English say things like "I mechanic." Because everything is laid out so carefully through declined noun and adjective and thoroughly conjugated verb, Russian does not feel the need for articles (a, an, the). "I mechanic" is a complete sentence.

Learning Issues
Due mainly to its radically different alphabet and complex grammatical structure, English speakers may not always find Russian easy to learn. It can also be difficult to distinguish between three different soft "i" sounds, and to master the gently rolling "r." Syllables are combined in ways unheard of in English, as in vsyeobshchee ("universal"). However, it is well worth the effort. It's a beautiful language.