Nouns: Case

First things first: If you don't already speak an inflected language (such as Latin or German), go to the Russian Language Mentor and read Fundamentals of Case Grammar. This will give you a better understanding of what's going on when Russian inflects for case.

Russian has six cases, answering six general questions:

Case Name	English name	Function	Questions
Nominative	Subject	actor or agent, doer	Who? What?
Genitive	Possessive	possessor	Of whom, whose? Of what?
Accusative	Objective	object, one/thing done to	Whom? What?
Dative	Objective	indirect object, recipient	To whom? To what?
Instrumental	Objective	accompaniment, thing used	With/by whom? With/by what?
Prepositional	Objective	location, thing talked about	About whom? About what? Where?

Notice that in English, 'whom' declines but 'what' doesn't, and that 'whom' has only two declined forms. That's pretty much the case across the board. English nouns only change to show possession. Pronouns also change when used as objects - that is, some of them do.

Now, on to the case forms.

The dictionary form of the noun, the one you will learn in vocabulary lists and such, is the nominative case. (In English, this is often called "the subject(ive) case".) All subjects and all predicate nominatives are in nominative case. It is the basic form, the one all other forms change from.

The patterns of a noun's changing are called its declension. Generally, people say the endings are added to the noun; in practice, this is true for masculine nouns, but feminine and neuter nouns have their endings changed.

As an example, the full set for masculine стол table and feminine книга book:
стол стола стола столу столом столе столы столов столы столам столами столах
книга книги книгу книге книгой книге книги книг книги книгам книгами книгах
Note how the -a from книга disappears and is replaced by the other endings. (Don't fear! We will go into all the cases and their endings.)

Posts by Case:
Prepositional:

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Resources  

Here is a web application that will provide all the forms of a noun you provide.

These language learning sites will have units on noun cases: Master Russian, Russian Nouns and Cases.

From Learning Russian,Nouns and Cases.

From Russian Lessons, Summary of the Cases with more details at links provided.