Articles
There is only one definite article in English, "the". There are six 'articoli ' in Italian, plus one contracted form:
"il" is the masculine singular article. It is the most frequent as it occurs before all the words beginning with a consonant except those described in point 2 below: il bambino, il mio libro, il giornale, etc.;
"lo", also m. sing., is used instead of "il" before words beginning with "z" or by "s" followed by another consonant: lo zucchero, lo zaino, lo scolaro, lo stesso giorno, etc.
"l' " is the contracted form of "lo" and is used before all the m. words beginning with a vowel: l'albero, l'elefante, l'onore, etc.;
"la" is the feminine singular article, before all feminine words beginning with a consonant: la casa, la mano, la nave, etc.;
"l' " is also the contracted form of "la" and is used before all the f. words beginning with a vowel: l'amica, l'oliva, l'isola, etc.;
The plural of "il" is "i": i bambini, i miei libri, i giornali...
The plural of "lo, l' (m.)" is "gli": gli zuccheri, gli zaini, gli scolari, gli stessi giorni, gli alberi, gli elefanti, gli onori...
The plural of "la, l' (f.)" is "le": le case, le mani, le navi, le amiche, le olive, le isole...
There is only one indefinite article in English, in two forms "a, an" chosen on the basis of the following sound. There are three 'articoli indeterminativi' in Italian, plus one contracted form:
"un" is the masculine indefinite article. It is the most frequent as it occurs before all the words except those described in point 2 below: un bambino, un mio libro, un giornale, un albero, un elefante, un onore, etc.;
"uno", also m., is used instead of "un " before words beginning with "z" or by "s" followed by another consonant: uno zucchero, uno zaino, uno scolaro, uno stesso giorno, etc.;
"una" is the feminine indefinite article, before all feminine words beginning with a consonant: una casa, una mano, una nave, etc.;
"un' " is the contracted form of "una" and is used before feminine words beginning with a vowel: un'amica, un'oliva, un'isola, etc.;
Important remarks
Notice the difference between "un amico" (a male friend - no apostrophe) vs. un'amica (a female friend - with apostrophe). "un' " is only f., because the m. gender has "un" as a different form from "uno".
Accordingly, "un insegnante, un artista" are men while "un'insegnante, un'artista" are women.
"Uno" is also the number one. Only the makes it clear whether we are talking about "one whatever" or "just one". "Passami una scatola" 
Pass me a box; "Per favore, una scatola e due barattoli" One box and two cans, please.
The "plural" of the indefinite article ( Eng. "some" and related forms) is dealt with under "indefinite adjectives and pronouns" 
On the differences in the use of articles