Днём я обычно работаю дома.

During the day I usually work at home.

Breakdown of Днём я обычно работаю дома.

• я: I
• дома: at home
• работать: to work
• обычно: usually

Questions & Answers about Днём я обычно работаю дома.

Why is it Днём and not день at the beginning?

Днём is the instrumental case of день (“day”) used with a time meaning: “in/at the daytime.”
Russian often uses the instrumental to talk about parts of the day: утром (in the morning), днём (in the daytime), вечером (in the evening), ночью (at night).
So Днём я обычно работаю дома is literally “By-day I usually work at home,” which corresponds to English “During the day I usually work at home.”

What case is днём, and when do I use this form?

Днём is instrumental singular of день.
With time expressions, the instrumental can answer “when?” for broad periods: утром, днём, вечером, ночью.
You use this form when you mean “in the morning / during the day / in the evening / at night” in a general, habitual sense, without a specific clock time.

Why is there no preposition before днём? Why not в днём or something similar?

Here днём is already an adverb-like form; it doesn’t need a preposition.
В днём is ungrammatical.
If you want a more explicit phrase with a preposition, you’d normally switch to a different structure, for example: в течение дня (“during the day”), днём, в рабочее время (“during the day, in working hours”), etc.