Learn Spanish (Latin America): Trabajo todos los días.

In Spanish, to say "every day," you literally say "all the days" (todos los días). This is a set phrase. You will see this pattern with other time periods too, like todos los meses (every month) or todas las semanas (every week).

Since días ends in an 'a' (before the 's'), shouldn't it be las días?

That is a very common trap! The word día (day) is an exception to the normal gender rules. Even though it ends in -a, it is a masculine word. Because of this, it always takes masculine articles: el día (the day) and los días (the days).

Where is the word for "I" in this sentence?

The word for "I" is yo, but it is usually dropped in Spanish. The verb trabajo already ends in -o, which tells us exactly who is working. You could say Yo trabajo todos los días, but leaving yo out is perfectly clear and sounds much more natural.

Does the los in todos los días work like the el in el lunes (on Monday)?

Exactly! Just like you need the definite article (el) to talk about things happening on a specific day (el lunes = on Monday), you also need the plural article (los) when talking about all the days (todos los días). Spanish uses "the" with time expressions much more often than English does.