Latin nouns come in many types and flavors. Unlike English nouns, Latin nouns have many endings that clarify their use in a sentence. In English you could say:

The cat walks to the shop.

 In this case 'cat' is the subject and 'shop' is the (direct) object
 
 The subject is the noun that 'verbs', the direct object is the noun that gets 'verbed'. You can replace 'verb' there with the main verb of your sentence.
 
 The function of each noun is clarified by its position relative to other nouns in the sentence. This becomes visible if you swap two nouns around in the sentence, for example:

The shop walks to the cat.

 In this case 'shop' is the subject and 'cat' is the (direct) object.
 
 In Latin, the order does not matter. This is why many people say that you cannot translate Latin left to right. In order to clarify the meaning of the noun in Latin, the noun must be declined.
 
To decline a noun, you add an ending that is associated with the nouns function in the sentence. Let's say that -o means that the noun is the subject and -a means that the noun is the (direct) object.
 
Now we can say:

The cato walks to the shopa.

 or

The shopa walks to the cato.

 and they mean the same thing. You can even say:

Walks to cato the shopa.

 There are five basic cases in Latin, each with a different function. They are:
 The nominative (nom) is the subject.
The genitive (gen) indicates possession. It can often be translated with '-'s'
The dative (dat) is the indirect object. It can often be translated with 'to' or 'for'.
The accusative (acc) is the direct object.
The ablative (abl) is the subject of the preposition. It can often be translated with 'with',  'by' or 'from'.
 
Here is an English sentence with the equivalent Latin cases:

The cat's friend walks to the shop with the dog on Monday.

 cat's = genitive
 friend = nominative
 shop = accusative
 dog = dative
 Monday = ablative

 But how do you identify which case is which in a Latin text? You can do this by checking the ending, like the example from earlier. However, in Latin the ending can depend on more then just the case. There are four aspects to a Latin noun: the case, the declension, the gender, and the number.
 
 The case is the most complicated aspect, but we have already covered those.
The declension does not effect the translation, but is only there to make the language look and sound nicer and more fluid. There are five declensions.
The gender also does not effect the translation, it is in that way similar to French or German. The grammatical genders in Latin are the feminine, masculine, and neuter.
The number effects how many of the noun there is (like adding '-s' in English). The numbers in Latin (and in English) are the singular and plural.

Here is an example of a declension table in Latin:

(declension) declension group 1:
 (gender)       feminine:
 (number)      singular:
(case)           nom: -a
(case)           gen: -ae
(case)           dat: -ae
(case)           acc: -am
(case)           abl: -a

(number)      plural:
(case)           nom: -ae
(case)           gen: -arum
(case)           dat: -is
(case)           acc: -as
(case)           abl: -is
 
> Tables like this one often have the accusative in the second place, make sure to check the chart you are using to make sure which is which! <
 
Here are some examples of the table in use:
If you see the word 'puella' you can tell it is in the nominative or ablative singular.
If you see the word 'puellas' you can tell it is in the accusative plural.
 
The table above only shows the endings for nouns in the first declension. A declension can include all three grammatical genders, or just one (like the first declension). The second declension, for example, has two grammatical genders, the masculine and the neuter.
 
Here is an example translation:

Puella in villa cum amica suus ambulant.

 Puella = girl
 amicae = friend
 suus = his/her/their
 in = to
 villa = house
 ambulant = walk
 cum = with (when next to ablative)
 
 The translation is:

The girl walks to the house with her friend.

 Puella is nominative
 villa is accusative
 amicae is ablative

 Pronouns come in many types, but they all hold one thing in common; they replace a noun in the sentence. Because pronouns are basically nouns with special meanings, they also work like nouns grammatically. As an example, here is a table of the singular first person pronouns in Latin:
 
 nom:   ego
 gen:    mei
 dat:     mihi
 acc:    me
 abl:     me
 
 As you can see, this looks a lot like a noun declension table, however the forms are irregular and are not part of one of the five main declensions. Some pronouns, like the possessive pronoun, are treated like nouns in the sentence but are conjugated like verbs. For more information about this, read the 'pronouns' article on this site.