Learn Spanish (Latin America): Cocino pasta para la cena.

In Spanish, the ending of the verb tells you who is doing the action. The -o ending in cocino means "I cook", so the word yo (I) isn't strictly necessary. You could say Yo cocino pasta, but Spanish speakers usually drop the pronoun.

Why is there no la before pasta?

Just like in English, when you are talking about an unspecified amount of food (some pasta, rather than a specific plate of pasta), you don't need the article. You are just cooking "pasta" in general.

Why do we use para instead of por to mean "for" here?

The word para is used here because it shows the purpose or destination of the action. You are cooking the pasta specifically intended for dinner. When "for" means "intended for" or "for the purpose of", you usually need para.

Why do we say para la cena instead of just para cena?

In Spanish, you usually include the definite article (la) before the names of meals when they follow a preposition like para. It translates literally as "for the dinner," which is just the standard way to say "for dinner" in Spanish.