A number of French verbs take a direct object, while their English equivalents take a preposition, e.g. attendre (wait for); chercher (look for); demander (ask for); écouter (listen to); espérer (hope for); ignorer (be ignorant of); payer (pay for); regarder (look at); reprocher (reproach for).

Regarding payer in particular two cases are distinguished:

1) Payer If only one object, accusative.

pay someone, something, pay for something

E.g.

J’ai payé le propriétaire (I payed the proprietor).

J’ai payé mes dettes (I payed my debts).

J’ai payé le dîner (I have payed for the dinner).

2) Payer à If two objects, person in dative.

Pay (for something) for someone,

pay someone (for something)

E.g.

J’ai payé le dîner à mon frère (I have paid for the dinner for my brother).

J’ai payé 800 euros au (=à+le) propriétaire (I have paid the proprietor 800 euros.)

Je le lui ai payé 1000 euros (I have paid him 1000 euros for it).

Source: A French Reference Grammar, H. Ferrar. Oxford University Press (2nd Edition 1967). pp. 100, 108.

In addition to the other answer: you can also sometimes use “payer pour”. For example if you have committed a crime and have been to jail for it, then you can say “j’ai payé pour mon crime”. More generally you can “pay for”, “payer pour”, something bad you have done.

It’s also possible to say “payer pour quelqu’un” when you are “paying” for someone else’s mistakes, e.g. “il a menti et maintenant c’est moi qui paie”, “he lied and now I’m paying for it”.