Learn Russian: Инженер работает на заводе.

While в is usually used for being inside a building, завод (factory) is a special exception in Russian. You always use на (which usually means "on") when talking about working at or going to a factory.

Why is there an -е at the end of заводе?

The dictionary form of the word is завод. When talking about location (where something happens), Russian uses the Prepositional case. For most masculine nouns ending in a consonant, you make this case by adding -е to the end.

How do I know to use работает instead of работать?

Работать is the dictionary form (to work). Because the engineer (a "he" or "she") is doing the action right now, you need the matching present tense ending. You drop the -ть and add -ет to make работает (works).

Why is there no Russian word for "The" in front of инженер?

Russian does not use articles like "a", "an", or "the". Whether it translates to "an engineer" or "the engineer" is understood purely from the context of the conversation.