We use ONE instead of repeating a noun. We use ONE for singular nouns, and ONES for plurals.
 
- What beautiful flowers! Can I have one?  (one=flower)
- Who is your girlfriend? - The one in the red shirt
- I'd like a hamburger. One with lots of onion, please.
- Would you like to try these shoes, sir? - No, the black ones, please.
- Natural flowers are much better than artificial ones.
- Look at those children. The ones playing football. They're from San Francisco.

We don't use ONE for uncountable nouns, we use SOME (or nothing if it goes with an adjective)

- If you like mangos, I can give you one.
- If you like brown sugar, I can give you some.
- If you don't like French wine, we can buy Spanish (not: Spanish one)

Some grammatical words, etc can be used with a noun or alone, so they don't need to use ONE

- Which do you like?   (also: which one)
- He is the tallest (also: he is the tallest one)
- That's your book and this is mine  (not: my one)
- Banana or apple? - I'll take both  (not: both ones)
- I need more dollars, I have few  (not: few ones)

NOTE FOR SPANISH SPEAKERS

En español, cuando queremos evitar repetir el sustantivo, en la mayoría de los casos simplemente lo suprimimos y ya está, así que hay que tener cuidado porque en inglés casi nunca se puede suprimir.
 
1 - Which is your boy? - The one in the blue coat  (one=boy)  = ¿cuál es tu niño? - el del abrigo azul
2 - I want a cake. A big one with lots of cream  (one= cake)  = quiero una tarta. Una grande con mucha nata
 
En el ejemplo 1 el español sustantiva el artículo EL y en el ejemplo 2 sustantivamos el adjetivo GRANDE. En inglés ni los artículos ni los adjetivos pueden sustantivarse, tienen que ir siempre acompañando a un nombre; por eso si no queremos repetir el nombre usamos ONE, plural: ONES.
 
- I like those shoes. The ones near the window = me gustan esos zapatos. Los de al lado del escaparate
- Green apples often taste better than red ones = las manzanas verdes suelen saber mejor que las rojas