Learn Russian: Я работаю в понедельник.

While в often means 'in', Russian uses it to mean 'on' when talking about days of the week. To say 'on Monday', you use в followed by the Accusative case: в понедельник.

If в понедельник is in the Accusative case, why doesn't the word change from its dictionary form?

Понедельник is a masculine, inanimate noun (an abstract concept, not a living thing). In Russian, masculine inanimate nouns do not change their endings in the Accusative case. They look exactly the same as they do in the Nominative (dictionary) case!

If I want to ask someone when they work, how do I ask the question this sentence answers?

You would use the question word когда (when). To ask 'When do you work?', you would say Когда ты работаешь?. The phrase в понедельник is the standard way to answer a когда question about a day of the week.

Why does the verb end in -ю (работаю)?

The dictionary form of the verb is работать (to work). Because the subject of the sentence is я (I), you drop the -ть ending and add -ю so the verb grammatically matches the subject 'I'.