Learn Spanish (Latin America): Se necesitan unos zapatos nuevos para correr.

In Spanish, when you use the impersonal se (like saying "are needed" or "one needs"), the verb must match the thing being discussed. Since unos zapatos (shoes) is plural, the verb is the plural necesitan. If it were just one shoe, it would be se necesita un zapato.

Who is actually doing the needing in this sentence?

Nobody specific! The se here makes the sentence impersonal. It is a general statement meaning "are needed" or "people need". It focuses on what is required (zapatos nuevos), rather than who requires them.

The English translation says "to run", but couldn't para correr also mean "for running"?

Yes! In English, we often say "for running". But in Spanish, whenever a verb directly follows a preposition like para (for / in order to), it must stay in its infinitive (dictionary) form, which is correr here. You never use the -ndo form (like corriendo) directly after a preposition.

What does unos add to the sentence?

Unos literally means "some". While you could just say se necesitan zapatos nuevos (new shoes are needed), adding unos makes it sound a bit more natural, like saying "some new shoes" or "a pair of new shoes" in English.