Indeterminativo vs determinativo

Question

When do you use "un, uno, una, un'" over "il, lo, la, l', i, gli, le"? Such as why is "Una" used over "La" in this sentence; "Una nuova casa è grande o piccola?". And lastly does the article "Una" depend on the gender of "nuova" or "casa" ?

Answer 1

Most of this answer is derived from

Dardano, Trifone Grammatica italiana con nozioni di linguistica (1995), Zanichelli

For more in depth analyses of this subject I recommend to peruse the various questions on this website with the article tag. Good ones are this one or this one. Moreover there are extensive essays on the topic on the website of the Treccani Encyclopedia. Feel free to ask more specific questions as needed.

Articles in Italian

The usage of articles in Italian is a complex subject, which I cannot hope to completely cover in a Stackexchange answer, but I'll do my best to give a general survey useful for a beginner.

Articles are small particles that are used before nouns to specify the type of instance of the noun we are talking about. Italian articles are divided in three types: determinative, indeterminative and partitive. Articles are declined and agree with the corresponding noun in gender and number (so in la nuova casa, the article la needs to agree with casa, as does nuova).

Articles are never used in standard Italian before proper nouns (but it is common in some regional variants), except when the article is part of the noun itself (e.g. in the name of the city of La Spezia).

Determinative articles

| Masculine singular | Feminine singular | Masculine plural | Feminine plural |
-------------------------------------------------------------------------------
|     Il / lo        |        La         |       I/ Gli     |  Le             |

The determinative article is used to denote that the noun is used to refer to a particular instance of it. For example

Sto leggendo il libro. (I'm reading the book)

In this sentence we are saying that we are reading a specific book, the one I have been telling you about, not just any random book. This is by far the most common usage of the determinative article.

However, the determinative article can be used also for general statements and abstractions in which in English one would use the zero article:

L'uomo è un mammifero (Man is a mammal)

Here we use the definite article to say that Man, as a specie or abstract concept is a mammal, not that this particular man is a mammal.

The determinative article has also sometimes the value of demonstrative adjective.

Tra i due vestiti, preferisco il rosso (Between the two dresses, I prefer the red one)

(compare with Tra i due vestiti, preferisco quello rosso).

Indeterminative articles

| Masculine singular | Feminine singular |
 -----------------------------------------
|      Un/Uno        |       Una         |

The indeterminative article is used when we want to denote an unspecified instance of the noun

Sto leggendo un libro (I'm reading a book)

Here the book we're reading is not important. We probably never spoke about it before, it's just any random book.

The indeterminative article can also be used to make statements about a generic element of a group

Un cane non potrebbe mai convivere con un gatto (A dog could never live with a cat)

Compare with I cani non potrebbero mai convivere con i gatti (Dogs could never live with cats). In the first sentence we are talking about a generic dog, in the second we are making a statment about dogs as a class of beings. This difference is however rather subtle.

A final usage of the indeterminative article is as an intensifier

Aveva una faccia... (He had such a face)

The indeterminative article has no plural forms. In the case where a plural indeterminative article is needed, the partitive article or the indefinite adjectives qualche and alcuni are used instead.

Partitive articles

| Masculine singular | Feminine singular | Masculine plural | Feminine plural |
-------------------------------------------------------------------------------
|      Del/Dello     |       Della       |    Dei/Degli     |   Delle         |

The partitive article is used when we want to talk abut a quantity of something. It is the analog of English a bit of, some and of the partitive genitive of languages with cases.

Vado a comprare del latte (I'm going to buy some milk)

As said before, at the plural the partitive article can be used instead of the nonexistent plural indeterminative article.

Sento dei rumori (I hear noises)

These two usages can have sometimes very different meanings:

Vado a comprare del gelato (I'm going to buy some ice-cream)

Vado a comprare dei gelati (I'm going to buy ice-creams)

The partitive article is sometimes omitted when the noun it refers to is a subject or direct object postponed to the verb

Mi è rimasto solo [del] pane (Only some bread is left)

Ho mangiato [della] pasta (I ate [some] pasta)

Omitting the article

Sometimes in Italian a noun is used without an article. There is no real rule for when this happens, but it is often after a preposition or a verb. Unfortunately, there's no real recourse except memorizing those expressions. You can find an in-depth description of the various use cases in this article. Here are a few examples:

Giocare a calcio (To play football)

Essere in pigiama (To wear a pajama)

Senza + noun (Without), e.g. Senza dignità (Without dignity)

Parlare italiano (To speak Italian)

Answer 2

1) As @DaG suggested in comments, it's the same difference you find in the English language between "an" and "the".
If you use definite articles you're talking about a specific thing ("la casa nuova" means "that specific new house"), if you use indefinite articles you're just talking in general ("una casa nuova" is more like "a new house as many others").
2) The article depends on the gender of the subject (casa), not on the gender of its adjectives (nuova).

ps. notice how I sorted the words in my example. Even though you can say "nuova casa", we usually say "casa nuova", with the adjective after the subject.