In Spanish, when we express I like, we are not doing the action; we are receiving it from whatever is being liked. This is easier to see if we think of the verb to please:
I like NYC. Subject: I. Object: NYC.
NYC pleases me. Subject: NYC. Object: me.
In Spanish we follow the second example:
Me gusta NYC. Subject: NYC. Object: Yo.
We don’t use the subject pronoun (yo, tú) when using gustar. If we want to use a pronoun, we need to use the personal a in front of it (since the object, the one being pleased, is a person) and thus use the pronouns we use after a preposition. We will say a mí, a ti, a él, a nosotros, a vosotros, or a ellos.
We are also going to use a new set of pronouns (they are very similar to the reflexive pronouns):
(A mí) Me gusta / Me gustan
(A ti) Te gusta / Te gustan
(A él) Le gusta / Le gustan
(A nosotros) Nos gusta / Nos gustan
(A vosotros) [Os gusta / Os gustan]
(A ellos) Les gusta / Les gustan
Examples
Me gustan las manzanas.* (I like apples.) or (Apples please me.)
Le gusta Laura. (He/she likes Laura.) or (Laura pleases him/her.)
Nos gusta mucho la comida. (We like food a lot.) or (Food pleases us a lot.)
Note: We are not required to use the pronouns a mí, a ti, etc. unless we want to emphasize the person: Me gustan las manzanas. Juan, ¿a ti te gustan las manzanas?
When we use a noun, we must use the preposition a in front of it:
A Pedro le gustan las manzanas.
A mi hermano no le gusta la pizza.
When we want to say activities we like, we use the infinitive of the verb:
Me gusta cantar. A mi hermano no le gusta trabajar.
* Important: when using generic/uncountable nouns with gustar we must always use a definite article (el, la, los, las):
Me gusta la piña (I like pineapple).
Me gustan los gatos (I like cats).
