In Latin there is no indefinite or definite article. They can be replaced by other adjectivals such as ille (froms of ille gradually changed into simply le or la like what we have in the modern Romance languages today), haec, ea, id, is etc.
Nouns and Adjectives
All adjectives must agree with the noun it describes in number, case and gender. All nouns are either feminine, masculine, or neuter. Genders are grammatical, and do not necessarily correspond to the sex of the object.
There are 5 declensions. Most nouns in the 1st are feminine, most in the 2nd are masculine and neuter (usually destinguished by the m. -us and n. -um endings), 3rd can either be masculine, feminine, or neuter, 4th is either masculine or feminine, and 5th is usually feminine with some masculine. Basically, you will have to learn the gender of each noun independently. For each noun, make sure you know which declension it is in, in order to decline it, and what gender it is, so that adjectives agree.
Adjectives are either 1/2nd declension or 3rd declension. In 1/2nd declensions, -a endings are treated as feminine and are declined like 1st declension nouns, and -us endings are treated as masculine, and -um endings are treated as neuter and both are declined like second declension nouns.
For example:
Cornelia bona (feminine) (good Cornelia) Cornelius bonus (masculine) (good Cornelius) bellum bonum (neuter) (good war)
In 3rd declension adjectives, for masculine and feminine, most of the time there are no changes which are needed to be made to match gender as both masculine and feminine decline the same (make note that in the ablative usually you use an -i instead of -e as most 3rd declension adjectives are -i stemmed.). Neuter has one important difference, as nominative and accussative in all declensions are the same (-um for 2nd etc.) and for plural nominative and accussative have -a (all neuters in all declensions do this as well).
Adjectives can also have comparative forms and superlative forms. Fortior is 'braver' (comparative). Fortissimus is 'bravest' (superlative). Basically, you drop the ending (-a, -us, -um) and place -ior to get the comparative ('braver') or add -issimus to make 'most brave'.
Cornelia est fortior quam Cornelius. Cornelia is braver than Cornelius. (quam after a comparative is 'than', otherwise it usually is feminine singular relative pronoun). Cornelia est fortissimus. Cornelia is the bravest.
On the noun tables there are usually 5 declensions:
Nominative-Used to show the subject of the sentence: Cornelia is a girl.
Genitive-Used to show posession (most of the time): The hair of Cornelia is long.
Dative-Used to show an indirect object: He gave the cookie to the boy.
Accusative-Used to show a direct object: Cornelia killed Marcus.
Also can be used with a preposition: We went into the bedroom.
Ablative-Has very many uses:
Can be used with a preposition: He is inside the palace.
Can be used to show time: At the tenth hour he died. (No preposition needed)
Can show manner: He beat me with a stick. (No preposition needed)
Can show means: He yelled with a great voice. (No preposition needed)
Can also be used with a passive verb: The cookie was thrown by Cornelia across the room. (No preposition needed)
There are many more uses for the ablative case.
And sometimes you may come across the vocative case, used in direct address.
There is also something called the locative case, used to describe the location of something. However, only a few nouns survived (such as domus).