Learn Russian: Он купил пакет помидоров.

We use the Genitive case after containers and words of quantity to mean 'of something'. Since a bag holds multiple tomatoes, we use the Genitive plural form.

How exactly do we get the -ов ending on помидоров?

The dictionary form is помидор, which is a masculine noun ending in a hard consonant. The rule for the Genitive plural of regular masculine nouns ending in a hard consonant is to simply add -ов.

Пакет is the direct object (the thing he bought). Why doesn't its ending change?

Direct objects take the Accusative case. For inanimate masculine nouns like пакет (a bag or packet), the Accusative form is identical to the dictionary form. It would only take a different ending if the noun were a living thing.

Why does the sentence use the perfective verb купил rather than the imperfective покупал?

Купил is used because this was a single, successfully completed action. If you wanted to say 'he was buying' or 'he frequently bought' bags of tomatoes, you would use the imperfective verb покупал.